Critical Behavior of Spatial Evolutionary Game with Altruistic to Spiteful Preferences on Two-Dimensional Lattices

NASA Astrophysics Data System (ADS)

Yang, Bo; Li, Xiao-Teng; Chen, Wei; Liu, Jian; Chen, Xiao-Song

2016-10-01

Self-questioning mechanism which is similar to single spin-flip of Ising model in statistical physics is introduced into spatial evolutionary game model. We propose a game model with altruistic to spiteful preferences via weighted sums of own and opponent's payoffs. This game model can be transformed into Ising model with an external field. Both interaction between spins and the external field are determined by the elements of payoff matrix and the preference parameter. In the case of perfect rationality at zero social temperature, this game model has three different phases which are entirely cooperative phase, entirely non-cooperative phase and mixed phase. In the investigations of the game model with Monte Carlo simulation, two paths of payoff and preference parameters are taken. In one path, the system undergoes a discontinuous transition from cooperative phase to non-cooperative phase with the change of preference parameter. In another path, two continuous transitions appear one after another when system changes from cooperative phase to non-cooperative phase with the prefenrence parameter. The critical exponents v, β, and γ of two continuous phase transitions are estimated by the finite-size scaling analysis. Both continuous phase transitions have the same critical exponents and they belong to the same universality class as the two-dimensional Ising model. Supported by the National Natural Science Foundation of China under Grant Nos. 11121403 and 11504384

An extended approach for computing the critical properties in the two-and three-dimensional lattices within the effective-field renormalization group method

NASA Astrophysics Data System (ADS)

de Albuquerque, Douglas F.; Santos-Silva, Edimilson; Moreno, N. O.

2009-10-01

In this letter we employing the effective-field renormalization group (EFRG) to study the Ising model with nearest neighbors to obtain the reduced critical temperature and exponents ν for bi- and three-dimensional lattices by increasing cluster scheme by extending recent works. The technique follows up the same strategy of the mean field renormalization group (MFRG) by introducing an alternative way for constructing classical effective-field equations of state takes on rigorous Ising spin identities.

Recurrence relations in one-dimensional Ising models.

PubMed

da Conceição, C M Silva; Maia, R N P

2017-09-01

The exact finite-size partition function for the nonhomogeneous one-dimensional (1D) Ising model is found through an approach using algebra operators. Specifically, in this paper we show that the partition function can be computed through a trace from a linear second-order recurrence relation with nonconstant coefficients in matrix form. A relation between the finite-size partition function and the generalized Lucas polynomials is found for the simple homogeneous model, thus establishing a recursive formula for the partition function. This is an important property and it might indicate the possible existence of recurrence relations in higher-dimensional Ising models. Moreover, assuming quenched disorder for the interactions within the model, the quenched averaged magnetic susceptibility displays a nontrivial behavior due to changes in the ferromagnetic concentration probability.

Mapping of the Bak, Tang, and Wiesenfeld sandpile model on a two-dimensional Ising-correlated percolation lattice to the two-dimensional self-avoiding random walk.

PubMed

Cheraghalizadeh, J; Najafi, M N; Dashti-Naserabadi, H; Mohammadzadeh, H

2017-11-01

The self-organized criticality on the random fractal networks has many motivations, like the movement pattern of fluid in the porous media. In addition to the randomness, introducing correlation between the neighboring portions of the porous media has some nontrivial effects. In this paper, we consider the Ising-like interactions between the active sites as the simplest method to bring correlations in the porous media, and we investigate the statistics of the BTW model in it. These correlations are controlled by the artificial "temperature" T and the sign of the Ising coupling. Based on our numerical results, we propose that at the Ising critical temperature T_{c} the model is compatible with the universality class of two-dimensional (2D) self-avoiding walk (SAW). Especially the fractal dimension of the loops, which are defined as the external frontier of the avalanches, is very close to D_{f}^{SAW}=4/3. Also, the corresponding open curves has conformal invariance with the root-mean-square distance R_{rms}∼t^{3/4} (t being the parametrization of the curve) in accordance with the 2D SAW. In the finite-size study, we observe that at T=T_{c} the model has some aspects compatible with the 2D BTW model (e.g., the 1/log(L)-dependence of the exponents of the distribution functions) and some in accordance with the Ising model (e.g., the 1/L-dependence of the fractal dimensions). The finite-size scaling theory is tested and shown to be fulfilled for all statistical observables in T=T_{c}. In the off-critical temperatures in the close vicinity of T_{c} the exponents show some additional power-law behaviors in terms of T-T_{c} with some exponents that are reported in the text. The spanning cluster probability at the critical temperature also scales with L^{1/2}, which is different from the regular 2D BTW model.

The Ising Decision Maker: a binary stochastic network for choice response time.

PubMed

Verdonck, Stijn; Tuerlinckx, Francis

2014-07-01

The Ising Decision Maker (IDM) is a new formal model for speeded two-choice decision making derived from the stochastic Hopfield network or dynamic Ising model. On a microscopic level, it consists of 2 pools of binary stochastic neurons with pairwise interactions. Inside each pool, neurons excite each other, whereas between pools, neurons inhibit each other. The perceptual input is represented by an external excitatory field. Using methods from statistical mechanics, the high-dimensional network of neurons (microscopic level) is reduced to a two-dimensional stochastic process, describing the evolution of the mean neural activity per pool (macroscopic level). The IDM can be seen as an abstract, analytically tractable multiple attractor network model of information accumulation. In this article, the properties of the IDM are studied, the relations to existing models are discussed, and it is shown that the most important basic aspects of two-choice response time data can be reproduced. In addition, the IDM is shown to predict a variety of observed psychophysical relations such as Piéron's law, the van der Molen-Keuss effect, and Weber's law. Using Bayesian methods, the model is fitted to both simulated and real data, and its performance is compared to the Ratcliff diffusion model. (c) 2014 APA, all rights reserved.

Rényi information flow in the Ising model with single-spin dynamics.

PubMed

Deng, Zehui; Wu, Jinshan; Guo, Wenan

2014-12-01

The n-index Rényi mutual information and transfer entropies for the two-dimensional kinetic Ising model with arbitrary single-spin dynamics in the thermodynamic limit are derived as functions of ensemble averages of observables and spin-flip probabilities. Cluster Monte Carlo algorithms with different dynamics from the single-spin dynamics are thus applicable to estimate the transfer entropies. By means of Monte Carlo simulations with the Wolff algorithm, we calculate the information flows in the Ising model with the Metropolis dynamics and the Glauber dynamics, respectively. We find that not only the global Rényi transfer entropy, but also the pairwise Rényi transfer entropy, peaks in the disorder phase.

Numerical estimation of structure constants in the three-dimensional Ising conformal field theory through Markov chain uv sampler

NASA Astrophysics Data System (ADS)

Herdeiro, Victor

2017-09-01

Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016), 10.1103/PhysRevE.94.043322] introduced a numerical recipe, dubbed uv sampler, offering precise estimations of the conformal field theory (CFT) data of the planar two-dimensional (2D) critical Ising model. It made use of scale invariance emerging at the critical point in order to sample finite sublattice marginals of the infinite plane Gibbs measure of the model by producing holographic boundary distributions. The main ingredient of the Markov chain Monte Carlo sampler is the invariance under dilation. This paper presents a generalization to higher dimensions with the critical 3D Ising model. This leads to numerical estimations of a subset of the CFT data—scaling weights and structure constants—through fitting of measured correlation functions. The results are shown to agree with the recent most precise estimations from numerical bootstrap methods [Kos, Poland, Simmons-Duffin, and Vichi, J. High Energy Phys. 08 (2016) 036, 10.1007/JHEP08(2016)036].

A Short Note on the Scaling Function Constant Problem in the Two-Dimensional Ising Model

NASA Astrophysics Data System (ADS)

Bothner, Thomas

2018-02-01

We provide a simple derivation of the constant factor in the short-distance asymptotics of the tau-function associated with the 2-point function of the two-dimensional Ising model. This factor was first computed by Tracy (Commun Math Phys 142:297-311, 1991) via an exponential series expansion of the correlation function. Further simplifications in the analysis are due to Tracy and Widom (Commun Math Phys 190:697-721, 1998) using Fredholm determinant representations of the correlation function and Wiener-Hopf approximation results for the underlying resolvent operator. Our method relies on an action integral representation of the tau-function and asymptotic results for the underlying Painlevé-III transcendent from McCoy et al. (J Math Phys 18:1058-1092, 1977).

Critical behavior of magnetization in URhAl: Quasi-two-dimensional Ising system with long-range interactions

NASA Astrophysics Data System (ADS)

Tateiwa, Naoyuki; Pospíšil, Jiří; Haga, Yoshinori; Yamamoto, Etsuji

2018-02-01

The critical behavior of dc magnetization in the uranium ferromagnet URhAl with the hexagonal ZrNiAl-type crystal structure has been studied around the ferromagnetic transition temperature TC. The critical exponent β for the temperature dependence of the spontaneous magnetization below TC,γ for the magnetic susceptibility, and δ for the magnetic isotherm at TC, have been obtained with a modified Arrott plot, a Kouvel-Fisher plot, the critical isotherm analysis, and the scaling analysis. We have determined the critical exponents as β =0.287 ±0.005 , γ =1.47 ±0.02 , and δ =6.08 ±0.04 by the scaling analysis and the critical isotherm analysis. These critical exponents satisfy the Widom scaling law δ =1 +γ /β . URhAl has strong uniaxial magnetic anisotropy, similar to its isostructural UCoAl that has been regarded as a three-dimensional (3D) Ising system in previous studies. However, the universality class of the critical phenomenon in URhAl does not belong to the 3D Ising model (β =0.325 , γ =1.241 , and δ =4.82 ) with short-range exchange interactions between magnetic moments. The determined exponents can be explained with the results of the renormalization group approach for a two-dimensional (2D) Ising system coupled with long-range interactions decaying as J (r ) ˜r-(d +σ ) with σ =1.44 . We suggest that the strong hybridization between the uranium 5 f and rhodium 4 d electrons in the U-RhI layer in the hexagonal crystal structure is a source of the low-dimensional magnetic property. The present result is contrary to current understandings of the physical properties in a series of isostructural UTX uranium ferromagnets (T: transition metals, X: p -block elements) based on the 3D Ising model.

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice.

PubMed

Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

2016-10-10

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic-to-paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models.

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice

PubMed Central

Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

2016-01-01

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic–to–paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models. PMID:27721435

Shock probes in a one-dimensional Katz-Lebowitz-Spohn model

NASA Astrophysics Data System (ADS)

Chatterjee, Sakuntala; Barma, Mustansir

2008-06-01

We consider shock probes in a one-dimensional driven diffusive medium with nearest-neighbor Ising interaction (KLS model). Earlier studies based on an approximate mapping of the present system to an effective zero-range process concluded that the exponents characterizing the decays of several static and dynamical correlation functions of the probes depend continuously on the strength of the Ising interaction. On the contrary, our numerical simulations indicate that over a substantial range of the interaction strength, these exponents remain constant and their values are the same as in the case of no interaction (when the medium executes an ASEP). We demonstrate this by numerical studies of several dynamical correlation functions for two probes and also for a macroscopic number of probes. Our results are consistent with the expectation that the short-ranged correlations induced by the Ising interaction should not affect the large time and large distance properties of the system, implying that scaling forms remain the same as in the medium with no interactions present.

Entanglement entropy at infinite-randomness fixed points in higher dimensions.

PubMed

Lin, Yu-Cheng; Iglói, Ferenc; Rieger, Heiko

2007-10-05

The entanglement entropy of the two-dimensional random transverse Ising model is studied with a numerical implementation of the strong-disorder renormalization group. The asymptotic behavior of the entropy per surface area diverges at, and only at, the quantum phase transition that is governed by an infinite-randomness fixed point. Here we identify a double-logarithmic multiplicative correction to the area law for the entanglement entropy. This contrasts with the pure area law valid at the infinite-randomness fixed point in the diluted transverse Ising model in higher dimensions.

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

DOE PAGES

James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe; ...

2018-02-26

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme-tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one andmore » two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro-modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. Lastly, we describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.« less

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme-tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one andmore » two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro-modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. Lastly, we describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.« less

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

NASA Astrophysics Data System (ADS)

James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe; Robinson, Neil J.; Tsvelik, Alexei M.

2018-04-01

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb–Liniger model, 1  +  1D quantum chromodynamics, as well as Landau–Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.

New developments in the theoretical treatment of low dimensional strongly correlated systems.

PubMed

James, Andrew J A; Konik, Robert M; Lecheminant, Philippe; Robinson, Neil; Tsvelik, Alexei M

2017-10-09

We review two important non-perturbative approaches for extracting the physics of low- dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of confor- mal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme- tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro- modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics. © 2017 IOP Publishing Ltd.

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods.

PubMed

James, Andrew J A; Konik, Robert M; Lecheminant, Philippe; Robinson, Neil J; Tsvelik, Alexei M

2018-02-26

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1  +  1D quantum chromodynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.

Simulation of glioblastoma multiforme (GBM) tumor cells using ising model on the Creutz Cellular Automaton

NASA Astrophysics Data System (ADS)

Züleyha, Artuç; Ziya, Merdan; Selçuk, Yeşiltaş; Kemal, Öztürk M.; Mesut, Tez

2017-11-01

Computational models for tumors have difficulties due to complexity of tumor nature and capacities of computational tools, however, these models provide visions to understand interactions between tumor and its micro environment. Moreover computational models have potential to develop strategies for individualized treatments for cancer. To observe a solid brain tumor, glioblastoma multiforme (GBM), we present a two dimensional Ising Model applied on Creutz cellular automaton (CCA). The aim of this study is to analyze avascular spherical solid tumor growth, considering transitions between non tumor cells and cancer cells are like phase transitions in physical system. Ising model on CCA algorithm provides a deterministic approach with discrete time steps and local interactions in position space to view tumor growth as a function of time. Our simulation results are given for fixed tumor radius and they are compatible with theoretical and clinic data.

Emergent Ising degrees of freedom above a double-stripe magnetic ground state [Emergent Ising degrees of freedom above double-stripe magnetism

DOE PAGES

Zhang, Guanghua; Flint, Rebecca

2017-12-27

Here, double-stripe magnetism [Q=(π/2,π/2)] has been proposed as the magnetic ground state for both the iron-telluride and BaTi 2Sb 2O families of superconductors. Double-stripe order is captured within a J 1–J 2–J 3 Heisenberg model in the regime J 3 >> J 2 >> J 1. Intriguingly, besides breaking spin-rotational symmetry, the ground-state manifold has three additional Ising degrees of freedom associated with bond ordering. Via their coupling to the lattice, they give rise to an orthorhombic distortion and to two nonuniform lattice distortions with wave vector (π,π). Because the ground state is fourfold degenerate, modulo rotations in spin space,more » only two of these Ising bond order parameters are independent. Here, we introduce an effective field theory to treat all Ising order parameters, as well as magnetic order, and solve it within a large-N limit. All three transitions, corresponding to the condensations of two Ising bond order parameters and one magnetic order parameter are simultaneous and first order in three dimensions, but lower dimensionality, or equivalently weaker interlayer coupling, and weaker magnetoelastic coupling can split the three transitions, and in some cases allows for two separate Ising phase transitions above the magnetic one.« less

Emergent Ising degrees of freedom above a double-stripe magnetic ground state [Emergent Ising degrees of freedom above double-stripe magnetism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Guanghua; Flint, Rebecca

Here, double-stripe magnetism [Q=(π/2,π/2)] has been proposed as the magnetic ground state for both the iron-telluride and BaTi 2Sb 2O families of superconductors. Double-stripe order is captured within a J 1–J 2–J 3 Heisenberg model in the regime J 3 >> J 2 >> J 1. Intriguingly, besides breaking spin-rotational symmetry, the ground-state manifold has three additional Ising degrees of freedom associated with bond ordering. Via their coupling to the lattice, they give rise to an orthorhombic distortion and to two nonuniform lattice distortions with wave vector (π,π). Because the ground state is fourfold degenerate, modulo rotations in spin space,more » only two of these Ising bond order parameters are independent. Here, we introduce an effective field theory to treat all Ising order parameters, as well as magnetic order, and solve it within a large-N limit. All three transitions, corresponding to the condensations of two Ising bond order parameters and one magnetic order parameter are simultaneous and first order in three dimensions, but lower dimensionality, or equivalently weaker interlayer coupling, and weaker magnetoelastic coupling can split the three transitions, and in some cases allows for two separate Ising phase transitions above the magnetic one.« less

Spin waves, vortices, fermions, and duality in the Ising and Baxter models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ogilvie, M.C.

1981-10-15

Field-theoretic methods are applied to a number of two-dimensional lattice models with Abelian symmetry groups. It is shown, using a vortex+spin-wave decomposition, that the Z/sub p/-Villain models are related to a class of continuum field theories with analogous duality properties. Fermion operators for these field theories are discussed. In the case of the Ising model, the vortices and spin-waves conspire to produce a free, massive Majorana field theory in the continuum limit. The continuum limit of the Baxter model is also studied, and the recent results of Kadanoff and Brown are rederived and extended.

Emergent Ising degrees of freedom above a double-stripe magnetic ground state

NASA Astrophysics Data System (ADS)

Zhang, Guanghua; Flint, Rebecca

2017-12-01

Double-stripe magnetism [Q =(π /2 ,π /2 )] has been proposed as the magnetic ground state for both the iron-telluride and BaTi2Sb2O families of superconductors. Double-stripe order is captured within a J1-J2-J3 Heisenberg model in the regime J3≫J2≫J1 . Intriguingly, besides breaking spin-rotational symmetry, the ground-state manifold has three additional Ising degrees of freedom associated with bond ordering. Via their coupling to the lattice, they give rise to an orthorhombic distortion and to two nonuniform lattice distortions with wave vector (π ,π ) . Because the ground state is fourfold degenerate, modulo rotations in spin space, only two of these Ising bond order parameters are independent. Here, we introduce an effective field theory to treat all Ising order parameters, as well as magnetic order, and solve it within a large-N limit. All three transitions, corresponding to the condensations of two Ising bond order parameters and one magnetic order parameter are simultaneous and first order in three dimensions, but lower dimensionality, or equivalently weaker interlayer coupling, and weaker magnetoelastic coupling can split the three transitions, and in some cases allows for two separate Ising phase transitions above the magnetic one.

Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models

NASA Astrophysics Data System (ADS)

Steinhaus, Sebastian

2015-09-01

The universal coupling of matter and gravity is one of the most important features of general relativity. In quantum gravity, in particular spin foams, matter couplings have been defined in the past, yet the mutual dynamics, in particular if matter and gravity are strongly coupled, are hardly explored, which is related to the definition of both matter and gravitational degrees of freedom on the discretization. However, extracting these mutual dynamics is crucial in testing the viability of the spin foam approach and also establishing connections to other discrete approaches such as lattice gauge theories. Therefore, we introduce a simple two-dimensional toy model for Yang-Mills coupled to spin foams, namely an Ising model coupled to so-called intertwiner models defined for SU (2 )k. The two systems are coupled by choosing the Ising coupling constant to depend on spin labels of the background, as these are interpreted as the edge lengths of the discretization. We coarse grain this toy model via tensor network renormalization and uncover an interesting dynamics: the Ising phase transition temperature turns out to be sensitive to the background configurations and conversely, the Ising model can induce phase transitions in the background. Moreover, we observe a strong coupling of both systems if close to both phase transitions.

Semiconductor of spinons: from Ising band insulator to orthogonal band insulator.

PubMed

Farajollahpour, T; Jafari, S A

2018-01-10

We use the ionic Hubbard model to study the effects of strong correlations on a two-dimensional semiconductor. The spectral gap in the limit where on-site interactions are zero is set by the staggered ionic potential, while in the strong interaction limit it is set by the Hubbard U. Combining mean field solutions of the slave spin and slave rotor methods, we propose two interesting gapped phases in between: (i) the insulating phase before the Mott phase can be viewed as gapping a non-Fermi liquid state of spinons by the staggered ionic potential. The quasi-particles of underlying spinons are orthogonal to physical electrons, giving rise to the 'ARPES-dark' state where the ARPES gap will be larger than the optical and thermal gap. (ii) The Ising insulator corresponding to ordered phase of the Ising variable is characterized by single-particle excitations whose dispersion is controlled by Ising-like temperature and field dependences. The temperature can be conveniently employed to drive a phase transition between these two insulating phases where Ising exponents become measurable by ARPES and cyclotron resonance. The rare earth monochalcogenide semiconductors where the magneto-resistance is anomalously large can be a candidate system for the Ising band insulator. We argue that the Ising and orthogonal insulating phases require strong enough ionic potential to survive the downward renormalization of the ionic potential caused by Hubbard U.

Semiconductor of spinons: from Ising band insulator to orthogonal band insulator

NASA Astrophysics Data System (ADS)

Farajollahpour, T.; Jafari, S. A.

2018-01-01

We use the ionic Hubbard model to study the effects of strong correlations on a two-dimensional semiconductor. The spectral gap in the limit where on-site interactions are zero is set by the staggered ionic potential, while in the strong interaction limit it is set by the Hubbard U. Combining mean field solutions of the slave spin and slave rotor methods, we propose two interesting gapped phases in between: (i) the insulating phase before the Mott phase can be viewed as gapping a non-Fermi liquid state of spinons by the staggered ionic potential. The quasi-particles of underlying spinons are orthogonal to physical electrons, giving rise to the ‘ARPES-dark’ state where the ARPES gap will be larger than the optical and thermal gap. (ii) The Ising insulator corresponding to ordered phase of the Ising variable is characterized by single-particle excitations whose dispersion is controlled by Ising-like temperature and field dependences. The temperature can be conveniently employed to drive a phase transition between these two insulating phases where Ising exponents become measurable by ARPES and cyclotron resonance. The rare earth monochalcogenide semiconductors where the magneto-resistance is anomalously large can be a candidate system for the Ising band insulator. We argue that the Ising and orthogonal insulating phases require strong enough ionic potential to survive the downward renormalization of the ionic potential caused by Hubbard U.

Emergent 1d Ising Behavior in AN Elementary Cellular Automaton Model

NASA Astrophysics Data System (ADS)

Kassebaum, Paul G.; Iannacchione, Germano S.

The fundamental nature of an evolving one-dimensional (1D) Ising model is investigated with an elementary cellular automaton (CA) simulation. The emergent CA simulation employs an ensemble of cells in one spatial dimension, each cell capable of two microstates interacting with simple nearest-neighbor rules and incorporating an external field. The behavior of the CA model provides insight into the dynamics of coupled two-state systems not expressible by exact analytical solutions. For instance, state progression graphs show the causal dynamics of a system through time in relation to the system's entropy. Unique graphical analysis techniques are introduced through difference patterns, diffusion patterns, and state progression graphs of the 1D ensemble visualizing the evolution. All analyses are consistent with the known behavior of the 1D Ising system. The CA simulation and new pattern recognition techniques are scalable (in both dimension, complexity, and size) and have many potential applications such as complex design of materials, control of agent systems, and evolutionary mechanism design.

Effect of antifreeze protein on heterogeneous ice nucleation based on a two-dimensional random-field Ising model

NASA Astrophysics Data System (ADS)

Dong, Zhen; Wang, Jianjun; Zhou, Xin

2017-05-01

Antifreeze proteins (AFPs) are the key biomolecules that protect many species from suffering the extreme conditions. Their unique properties of antifreezing provide the potential of a wide range of applications. Inspired by the present experimental approaches of creating an antifreeze surface by coating AFPs, here we present a two-dimensional random-field lattice Ising model to study the effect of AFPs on heterogeneous ice nucleation. The model shows that both the size and the free-energy effect of individual AFPs and their surface coverage dominate the antifreeze capacity of an AFP-coated surface. The simulation results are consistent with the recent experiments qualitatively, revealing the origin of the surprisingly low antifreeze capacity of an AFP-coated surface when the coverage is not particularly high as shown in experiment. These results will hopefully deepen our understanding of the antifreeze effects and thus be potentially useful for designing novel antifreeze coating materials based on biomolecules.

The influence of further-neighbor spin-spin interaction on a ground state of 2D coupled spin-electron model in a magnetic field

NASA Astrophysics Data System (ADS)

Čenčariková, Hana; Strečka, Jozef; Gendiar, Andrej; Tomašovičová, Natália

2018-05-01

An exhaustive ground-state analysis of extended two-dimensional (2D) correlated spin-electron model consisting of the Ising spins localized on nodal lattice sites and mobile electrons delocalized over pairs of decorating sites is performed within the framework of rigorous analytical calculations. The investigated model, defined on an arbitrary 2D doubly decorated lattice, takes into account the kinetic energy of mobile electrons, the nearest-neighbor Ising coupling between the localized spins and mobile electrons, the further-neighbor Ising coupling between the localized spins and the Zeeman energy. The ground-state phase diagrams are examined for a wide range of model parameters for both ferromagnetic as well as antiferromagnetic interaction between the nodal Ising spins and non-zero value of external magnetic field. It is found that non-zero values of further-neighbor interaction leads to a formation of new quantum states as a consequence of competition between all considered interaction terms. Moreover, the new quantum states are accompanied with different magnetic features and thus, several kinds of field-driven phase transitions are observed.

Inverse Ising Inference Using All the Data

NASA Astrophysics Data System (ADS)

Aurell, Erik; Ekeberg, Magnus

2012-03-01

We show that a method based on logistic regression, using all the data, solves the inverse Ising problem far better than mean-field calculations relying only on sample pairwise correlation functions, while still computationally feasible for hundreds of nodes. The largest improvement in reconstruction occurs for strong interactions. Using two examples, a diluted Sherrington-Kirkpatrick model and a two-dimensional lattice, we also show that interaction topologies can be recovered from few samples with good accuracy and that the use of l1 regularization is beneficial in this process, pushing inference abilities further into low-temperature regimes.

The Critical Z-Invariant Ising Model via Dimers: Locality Property

NASA Astrophysics Data System (ADS)

Boutillier, Cédric; de Tilière, Béatrice

2011-01-01

We study a large class of critical two-dimensional Ising models, namely critical Z-invariant Ising models. Fisher (J Math Phys 7:1776-1781, 1966) introduced a correspondence between the Ising model and the dimer model on a decorated graph, thus setting dimer techniques as a powerful tool for understanding the Ising model. In this paper, we give a full description of the dimer model corresponding to the critical Z-invariant Ising model, consisting of explicit expressions which only depend on the local geometry of the underlying isoradial graph. Our main result is an explicit local formula for the inverse Kasteleyn matrix, in the spirit of Kenyon (Invent Math 150(2):409-439, 2002), as a contour integral of the discrete exponential function of Mercat (Discrete period matrices and related topics, 2002) and Kenyon (Invent Math 150(2):409-439, 2002) multiplied by a local function. Using results of Boutillier and de Tilière (Prob Theor Rel Fields 147(3-4):379-413, 2010) and techniques of de Tilière (Prob Th Rel Fields 137(3-4):487-518, 2007) and Kenyon (Invent Math 150(2):409-439, 2002), this yields an explicit local formula for a natural Gibbs measure, and a local formula for the free energy. As a corollary, we recover Baxter's formula for the free energy of the critical Z-invariant Ising model (Baxter, in Exactly solved models in statistical mechanics, Academic Press, London, 1982), and thus a new proof of it. The latter is equal, up to a constant, to the logarithm of the normalized determinant of the Laplacian obtained in Kenyon (Invent Math 150(2):409-439, 2002).

Dynamical behaviors of inter-out-of-equilibrium state intervals in Korean futures exchange markets

NASA Astrophysics Data System (ADS)

Lim, Gyuchang; Kim, SooYong; Kim, Kyungsik; Lee, Dong-In; Scalas, Enrico

2008-05-01

A recently discovered feature of financial markets, the two-phase phenomenon, is utilized to categorize a financial time series into two phases, namely equilibrium and out-of-equilibrium states. For out-of-equilibrium states, we analyze the time intervals at which the state is revisited. The power-law distribution of inter-out-of-equilibrium state intervals is shown and we present an analogy with discrete-time heat bath dynamics, similar to random Ising systems. In the mean-field approximation, this model reduces to a one-dimensional multiplicative process. By varying global and local model parameters, the relevance between volatilities in financial markets and the interaction strengths between agents in the Ising model are investigated and discussed.

A unified effective-field renormalization-group framework approach for the quenched diluted Ising models

NASA Astrophysics Data System (ADS)

de Albuquerque, Douglas F.; Fittipaldi, I. P.

1994-05-01

A unified effective-field renormalization-group framework (EFRG) for both quenched bond- and site-diluted Ising models is herein developed by extending recent works. The method, as in the previous works, follows up the same strategy of the mean-field renormalization-group scheme (MFRG), and is achieved by introducing an alternative way for constructing classical effective-field equations of state, based on rigorous Ising spin identities. The concentration dependence of the critical temperature, Tc(p), and the critical concentrations of magnetic atoms, pc, at which the transition temperature goes to zero, are evaluated for several two- and three-dimensional lattice structures. The obtained values of Tc and pc and the resulting phase diagrams for both bond and site cases are much more accurate than those estimated by the standard MFRG approach. Although preserving the same level of simplicity as the MFRG, it is shown that the present EFRG method, even by considering its simplest size-cluster version, provides results that correctly distinguishes those lattices that have the same coordination number, but differ in dimensionality or geometry.

Chiral Tricritical Point: A New Universality Class in Dirac Systems

NASA Astrophysics Data System (ADS)

Yin, Shuai; Jian, Shao-Kai; Yao, Hong

2018-05-01

Tricriticality, as a sister of criticality, is a fundamental and absorbing issue in condensed-matter physics. It has been verified that the bosonic Wilson-Fisher universality class can be changed by gapless fermionic modes at criticality. However, the counterpart phenomena at tricriticality have rarely been explored. In this Letter, we study a model in which a tricritical Ising model is coupled to massless Dirac fermions. We find that the massless Dirac fermions result in the emergence of a new tricritical point, which we refer to as the chiral tricritical point (CTP), at the phase boundary between the Dirac semimetal and the charge-density wave insulator. From functional renormalization group analysis of the effective action, we obtain the critical behaviors of the CTP, which are qualitatively distinct from both the tricritical Ising universality and the chiral Ising universality. We further extend the calculations of the chiral tricritical behaviors of Ising spins to the case of Heisenberg spins. The experimental relevance of the CTP in two-dimensional Dirac semimetals is also discussed.

A 16-bit Coherent Ising Machine for One-Dimensional Ring and Cubic Graph Problems

NASA Astrophysics Data System (ADS)

Takata, Kenta; Marandi, Alireza; Hamerly, Ryan; Haribara, Yoshitaka; Maruo, Daiki; Tamate, Shuhei; Sakaguchi, Hiromasa; Utsunomiya, Shoko; Yamamoto, Yoshihisa

2016-09-01

Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to finding a ground state of the Ising Hamiltonian, thus various physical systems have been studied to emulate and solve this Ising problem. Recently, networks of mutually injected optical oscillators, called coherent Ising machines, have been developed as promising solvers for the problem, benefiting from programmability, scalability and room temperature operation. Here, we report a 16-bit coherent Ising machine based on a network of time-division-multiplexed femtosecond degenerate optical parametric oscillators. The system experimentally gives more than 99.6% of success rates for one-dimensional Ising ring and nondeterministic polynomial-time (NP) hard instances. The experimental and numerical results indicate that gradual pumping of the network combined with multiple spectral and temporal modes of the femtosecond pulses can improve the computational performance of the Ising machine, offering a new path for tackling larger and more complex instances.

Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit.

PubMed

Huang, Bevin; Clark, Genevieve; Navarro-Moratalla, Efrén; Klein, Dahlia R; Cheng, Ran; Seyler, Kyle L; Zhong, Ding; Schmidgall, Emma; McGuire, Michael A; Cobden, David H; Yao, Wang; Xiao, Di; Jarillo-Herrero, Pablo; Xu, Xiaodong

2017-06-07

Since the discovery of graphene, the family of two-dimensional materials has grown, displaying a broad range of electronic properties. Recent additions include semiconductors with spin-valley coupling, Ising superconductors that can be tuned into a quantum metal, possible Mott insulators with tunable charge-density waves, and topological semimetals with edge transport. However, no two-dimensional crystal with intrinsic magnetism has yet been discovered; such a crystal would be useful in many technologies from sensing to data storage. Theoretically, magnetic order is prohibited in the two-dimensional isotropic Heisenberg model at finite temperatures by the Mermin-Wagner theorem. Magnetic anisotropy removes this restriction, however, and enables, for instance, the occurrence of two-dimensional Ising ferromagnetism. Here we use magneto-optical Kerr effect microscopy to demonstrate that monolayer chromium triiodide (CrI 3 ) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 kelvin is only slightly lower than that of the bulk crystal, 61 kelvin, which is consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phase, highlighting thickness-dependent physical properties typical of van der Waals crystals. Remarkably, bilayer CrI 3 displays suppressed magnetization with a metamagnetic effect, whereas in trilayer CrI 3 the interlayer ferromagnetism observed in the bulk crystal is restored. This work creates opportunities for studying magnetism by harnessing the unusual features of atomically thin materials, such as electrical control for realizing magnetoelectronics, and van der Waals engineering to produce interface phenomena.

Test of quantum thermalization in the two-dimensional transverse-field Ising model

PubMed Central

Blaß, Benjamin; Rieger, Heiko

2016-01-01

We study the quantum relaxation of the two-dimensional transverse-field Ising model after global quenches with a real-time variational Monte Carlo method and address the question whether this non-integrable, two-dimensional system thermalizes or not. We consider both interaction quenches in the paramagnetic phase and field quenches in the ferromagnetic phase and compare the time-averaged probability distributions of non-conserved quantities like magnetization and correlation functions to the thermal distributions according to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy in the system. We find that the occurrence of thermalization crucially depends on the quench parameters: While after the interaction quenches in the paramagnetic phase thermalization can be observed, our results for the field quenches in the ferromagnetic phase show clear deviations from the thermal system. These deviations increase with the quench strength and become especially clear comparing the shape of the thermal and the time-averaged distributions, the latter ones indicating that the system does not completely lose the memory of its initial state even for strong quenches. We discuss our results with respect to a recently formulated theorem on generalized thermalization in quantum systems. PMID:27905523

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barber, M.N.; Derrida, B.

We study the phase diagram of the two-dimensional anisotropic next-nearest neighbor Ising (ANNNI) model by comparing the time evolution of two distinct spin configurations submitted to the same thermal noise. We clearly se several dynamical transitions between ferromagnetic, paramagnetic, antiphase, and floating phases. These dynamical transitions seem to occur rather close to the transition lines determined previously in the literature.

Rotational Invariance of the 2d Spin - Spin Correlation Function

NASA Astrophysics Data System (ADS)

Pinson, Haru

2012-09-01

At the critical temperature in the 2d Ising model on the square lattice, we establish the rotational invariance of the spin-spin correlation function using the asymptotics of the spin-spin correlation function along special directions (McCoy and Wu in the two dimensional Ising model. Harvard University Press, Cambridge, 1973) and the finite difference Hirota equation for which the spin-spin correlation function is shown to satisfy (Perk in Phys Lett A 79:3-5, 1980; Perk in Proceedings of III international symposium on selected topics in statistical mechanics, Dubna, August 22-26, 1984, JINR, vol II, pp 138-151, 1985).

Critical Casimir force scaling functions of the two-dimensional Ising model at finite aspect ratios

NASA Astrophysics Data System (ADS)

Hobrecht, Hendrik; Hucht, Alfred

2017-02-01

We present a systematic method to calculate the universal scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer representation of the corresponding partition function Z on an L× M square lattice, wrapped around a torus with aspect ratio ρ =L/M . By assuming periodic boundary conditions and translational invariance in at least one direction, we systematically reduce the problem to a 2× 2 transfer matrix representation. For the torus we first reproduce the results by Kaufman and then give a detailed calculation of the scaling functions. Afterwards we present the calculation for the cylinder with open boundary conditions. All scaling functions are given in form of combinations of infinite products and integrals. Our results reproduce the known scaling functions in the limit of thin films ρ \\to 0 . Additionally, for the cylinder at criticality our results confirm the predictions from conformal field theory.

Revisiting 2D Lattice Based Spin Flip-Flop Ising Model: Magnetic Properties of a Thin Film and Its Temperature Dependence

ERIC Educational Resources Information Center

Singh, Satya Pal

2014-01-01

This paper presents a brief review of Ising's work done in 1925 for one dimensional spin chain with periodic boundary condition. Ising observed that no phase transition occurred at finite temperature in one dimension. He erroneously generalized his views in higher dimensions but that was not true. In 1941 Kramer and Wannier obtained…

Unsupervised machine learning account of magnetic transitions in the Hubbard model

NASA Astrophysics Data System (ADS)

Ch'ng, Kelvin; Vazquez, Nick; Khatami, Ehsan

2018-01-01

We employ several unsupervised machine learning techniques, including autoencoders, random trees embedding, and t -distributed stochastic neighboring ensemble (t -SNE), to reduce the dimensionality of, and therefore classify, raw (auxiliary) spin configurations generated, through Monte Carlo simulations of small clusters, for the Ising and Fermi-Hubbard models at finite temperatures. Results from a convolutional autoencoder for the three-dimensional Ising model can be shown to produce the magnetization and the susceptibility as a function of temperature with a high degree of accuracy. Quantum fluctuations distort this picture and prevent us from making such connections between the output of the autoencoder and physical observables for the Hubbard model. However, we are able to define an indicator based on the output of the t -SNE algorithm that shows a near perfect agreement with the antiferromagnetic structure factor of the model in two and three spatial dimensions in the weak-coupling regime. t -SNE also predicts a transition to the canted antiferromagnetic phase for the three-dimensional model when a strong magnetic field is present. We show that these techniques cannot be expected to work away from half filling when the "sign problem" in quantum Monte Carlo simulations is present.

Rise of pairwise thermal entanglement for an alternating Ising and Heisenberg spin chain in an arbitrarily oriented magnetic field

NASA Astrophysics Data System (ADS)

Rojas, M.; de Souza, S. M.; Rojas, Onofre

2014-03-01

Typically two particles (spins) could be maximally entangled at zero temperature, and for a certain temperature the phenomenon of entanglement vanishes at the threshold temperature. For the Heisenberg coupled model or even the Ising model with a transverse magnetic field, one can observe some rise of entanglement even for a disentangled region at zero temperature. So we can understand this emergence of entanglement at finite temperature as being due to the mixing of some maximally entangled states with some other untangled states. Here, we present a simple one-dimensional Ising model with alternating Ising and Heisenberg spins in an arbitrarily oriented magnetic field, which can be mapped onto the classical Ising model with a magnetic field. This model does not show any evidence of entanglement at zero temperature, but surprisingly at finite temperature rise a pairwise thermal entanglement between two untangled spins at zero temperature when an arbitrarily oriented magnetic field is applied. This effect is a purely magnetic field, and the temperature dependence, as soon as the temperature increases, causes a small increase in concurrence, achieving its maximum at around 0.1. Even for long-range entanglement, a weak concurrence still survives. There are also some real materials that could serve as candidates that would exhibit this effect, such as Dy(NO3)(DMSO)2Cu(opba)(DMSO)2 [DMSO = dimethyl sulfoxide; opba = o-phenylenebis(oxamoto)] [J. Strečka, M. Hagiwara, Y. Han, T. Kida, Z. Honda, and M. Ikeda, Condens. Matter Phys. 15, 43002 (2012), 10.5488/CMP.15.43002].

Critical scaling of the mutual information in two-dimensional disordered Ising models

NASA Astrophysics Data System (ADS)

Sriluckshmy, P. V.; Mandal, Ipsita

2018-04-01

Rényi mutual information, computed from second Rényi entropies, can identify classical phase transitions from their finite-size scaling at critical points. We apply this technique to examine the presence or absence of finite temperature phase transitions in various two-dimensional models on a square lattice, which are extensions of the conventional Ising model by adding a quenched disorder. When the quenched disorder causes the nearest neighbor bonds to be both ferromagnetic and antiferromagnetic, (a) a spin glass phase exists only at zero temperature, and (b) a ferromagnetic phase exists at a finite temperature when the antiferromagnetic bond distributions are sufficiently dilute. Furthermore, finite temperature paramagnetic-ferromagnetic transitions can also occur when the disordered bonds involve only ferromagnetic couplings of random strengths. In our numerical simulations, the ‘zero temperature only’ phase transitions are identified when there is no consistent finite-size scaling of the Rényi mutual information curves, while for finite temperature critical points, the curves can identify the critical temperature T c by their crossings at T c and 2 Tc .

Nonequilibrium two-dimensional Ising model with stationary uphill diffusion.

PubMed

Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia

2018-03-01

Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.

Nonequilibrium two-dimensional Ising model with stationary uphill diffusion

NASA Astrophysics Data System (ADS)

Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia

2018-03-01

Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.

Nature versus nurture: Predictability in low-temperature Ising dynamics

NASA Astrophysics Data System (ADS)

Ye, J.; Machta, J.; Newman, C. M.; Stein, D. L.

2013-10-01

Consider a dynamical many-body system with a random initial state subsequently evolving through stochastic dynamics. What is the relative importance of the initial state (“nature”) versus the realization of the stochastic dynamics (“nurture”) in predicting the final state? We examined this question for the two-dimensional Ising ferromagnet following an initial deep quench from T=∞ to T=0. We performed Monte Carlo studies on the overlap between “identical twins” raised in independent dynamical environments, up to size L=500. Our results suggest an overlap decaying with time as t-θh with θh=0.22±0.02; the same exponent holds for a quench to low but nonzero temperature. This “heritability exponent” may equal the persistence exponent for the two-dimensional Ising ferromagnet, but the two differ more generally.

Pushing the limits of Monte Carlo simulations for the three-dimensional Ising model

NASA Astrophysics Data System (ADS)

Ferrenberg, Alan M.; Xu, Jiahao; Landau, David P.

2018-04-01

While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from 163 to 10243. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature Kc=0.221 654 626 (5 ) and the critical exponent of the correlation length ν =0.629 912 (86 ) with precision that exceeds all previous Monte Carlo estimates.

Dynamic hysteresis in a one-dimensional Ising model: application to allosteric proteins.

PubMed

Graham, I; Duke, T A J

2005-06-01

We solve exactly the problem of dynamic hysteresis for a finite one-dimensional Ising model at low temperature. We find that the area of the hysteresis loop, as the field is varied periodically, scales as the square root of the field frequency for a large range of frequencies. Below a critical frequency there is a correction to the scaling law, resulting in a linear relationship between hysteresis area and frequency. The one-dimensional Ising model provides a simplified description of switchlike behavior in allosteric proteins, such as hemoglobin. Thus our analysis predicts the switching dynamics of allosteric proteins when they are exposed to a ligand concentration which changes with time. Many allosteric proteins bind a regulator that is maintained at a nonequilibrium concentration by active signal transduction processes. In the light of our analysis, we discuss to what extent allosteric proteins can respond to changes in regulator concentration caused by an upstream signaling event, while remaining insensitive to the intrinsic nonequilibrium fluctuations in regulator level which occur in the absence of a signal.

Universality of Critically Pinned Interfaces in Two-Dimensional Isotropic Random Media

NASA Astrophysics Data System (ADS)

Grassberger, Peter

2018-05-01

Based on extensive simulations, we conjecture that critically pinned interfaces in two-dimensional isotropic random media with short-range correlations are always in the universality class of ordinary percolation. Thus, in contrast to interfaces in >2 dimensions, there is no distinction between fractal (i.e., percolative) and rough but nonfractal interfaces. Our claim includes interfaces in zero-temperature random field Ising models (both with and without spontaneous nucleation), in heterogeneous bootstrap percolation, and in susceptible-weakened-infected-removed epidemics. It does not include models with long-range correlations in the randomness and models where overhangs are explicitly forbidden (which would imply nonisotropy of the medium).

Variational Approach to Monte Carlo Renormalization Group

NASA Astrophysics Data System (ADS)

Wu, Yantao; Car, Roberto

2017-12-01

We present a Monte Carlo method for computing the renormalized coupling constants and the critical exponents within renormalization theory. The scheme, which derives from a variational principle, overcomes critical slowing down, by means of a bias potential that renders the coarse grained variables uncorrelated. The two-dimensional Ising model is used to illustrate the method.

Quantum transitions driven by one-bond defects in quantum Ising rings.

PubMed

Campostrini, Massimo; Pelissetto, Andrea; Vicari, Ettore

2015-04-01

We investigate quantum scaling phenomena driven by lower-dimensional defects in quantum Ising-like models. We consider quantum Ising rings in the presence of a bond defect. In the ordered phase, the system undergoes a quantum transition driven by the bond defect between a magnet phase, in which the gap decreases exponentially with increasing size, and a kink phase, in which the gap decreases instead with a power of the size. Close to the transition, the system shows a universal scaling behavior, which we characterize by computing, either analytically or numerically, scaling functions for the low-level energy differences and the two-point correlation function. We discuss the implications of these results for the nonequilibrium dynamics in the presence of a slowly varying parallel magnetic field h, when going across the first-order quantum transition at h=0.

Absence of long range order in SrDy2O4 frustrated magnet due to trapped defects from a dimensionality crossover

NASA Astrophysics Data System (ADS)

Gauthier, Nicolas; Fennell, Amy; Uldry, Anne-Christine; Delley, Bernard; Sibille, Romain; White, Jonathan; Niedermayer, Christof; Pomjakushin, Vladimir; Kenzelmann, Michel; Prevost, Bobby; Desilets-Benoit, Alexandre; Bianchi, Andrea D.; Dabkowska, Hanna A.; Nilsen, Goran; Regnault, Louis-Pierre

The simultaneous occurence of geometrical frustration and low dimensionality can lead to strongly correlated fluctuating ground states. In the SrLn2O4 compounds, the Ln magnetic ions form one-dimensional (1D) zig-zag chains that have both of these characteristics, offering a playground to study novel states of matter. In SrDy2O4, the two inequivalent Dy3+ sites are Ising-like with perpendicular easy-axes, favouring the decoupling of neighbouring zig-zag chains. No long range order is observed down to T = 60 mK in zero field but diffuse neutron scattering indicates short range correlations that are consistent with those of the 1D Ising zig-zag chain model. AC susceptibility measurements indicate a slowing down of the fluctuations at low temperatures. We attribute this behaviour to the domain walls in the zig-zag chains. Experimental evidence of a dimensionality crossover at low temperatures in SrDy2O4 suggest that the domains walls are trapped because of interchain interactions, precluding long-range order to the lowest temperatures.

Frozen into stripes: fate of the critical Ising model after a quench.

PubMed

Blanchard, T; Picco, M

2013-09-01

In this article we study numerically the final state of the two-dimensional ferromagnetic critical Ising model after a quench to zero temperature. Beginning from equilibrium at T_{c}, the system can be blocked in a variety of infinitely long lived stripe states in addition to the ground state. Similar results have already been obtained for an infinite temperature initial condition and an interesting connection to exact percolation crossing probabilities has emerged. Here we complete this picture by providing an example of stripe states precisely related to initial crossing probabilities for various boundary conditions. We thus show that this is not specific to percolation but rather that it depends on the properties of spanning clusters in the initial state.

Three-dimensional analytical model for the spatial variation of the foreshock electron distribution function - Systematics and comparisons with ISEE observations

NASA Technical Reports Server (NTRS)

Fitzenreiter, R. J.; Scudder, J. D.; Klimas, A. J.

1990-01-01

A model which is consistent with the solar wind and shock surface boundary conditions for the foreshock electron distribution in the absence of wave-particle effects is formulated for an arbitrary location behind the magnetic tangent to the earth's bow shock. Variations of the gyrophase-averaged velocity distribution are compared and contrasted with in situ ISEE observations. It is found that magnetic mirroring of solar wind electrons is the most important process by which nonmonotonic reduced electron distributions in the foreshock are produced. Leakage of particles from the magnetosheath is shown to be relatively unimportant in determining reduced distributions that are nonmonotonic. The two-dimensional distribution function off the magnetic field direction is the crucial contribution in producing reduced distributions which have beams. The time scale for modification of the electron velocity distribution in velocity space can be significantly influenced by steady state spatial gradients in the background imposed by the curved shock geometry.

Quantum Monte Carlo study of the transverse-field quantum Ising model on infinite-dimensional structures

NASA Astrophysics Data System (ADS)

Baek, Seung Ki; Um, Jaegon; Yi, Su Do; Kim, Beom Jun

2011-11-01

In a number of classical statistical-physical models, there exists a characteristic dimensionality called the upper critical dimension above which one observes the mean-field critical behavior. Instead of constructing high-dimensional lattices, however, one can also consider infinite-dimensional structures, and the question is whether this mean-field character extends to quantum-mechanical cases as well. We therefore investigate the transverse-field quantum Ising model on the globally coupled network and on the Watts-Strogatz small-world network by means of quantum Monte Carlo simulations and the finite-size scaling analysis. We confirm that both of the structures exhibit critical behavior consistent with the mean-field description. In particular, we show that the existing cumulant method has difficulty in estimating the correct dynamic critical exponent and suggest that an order parameter based on the quantum-mechanical expectation value can be a practically useful numerical observable to determine critical behavior when there is no well-defined dimensionality.

Microscopic image processing systems for measuring nonuniform film thickness profiles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, A.H.; Plawsky, J.L.; DasGupta, S.

1994-01-01

In very thin liquid films. transport processes are controlled by the temperature and the interfacial intermolecular force field which is a function of the film thickness profile and interfacial properties. The film thickness profile and interfacial properties can be measured most efficiently using a microscopic image processing system. IPS, to record the intensity pattern of the reflected light from the film. There are two types of IPS: an image analyzing interferometer (IAI) and/or an image scanning ellipsometer (ISE). The ISE is a novel technique to measure the two dimensional thickness profile of a nonuniform, thin film, from 1 nm upmore » to several {mu}m, in a steady state as well as in a transient state. It is a full field imaging technique which can study every point on the surface simultaneously with high spatial resolution and thickness sensitivity, i.e., it can measure and map the 2-D film thickness profile. Using the ISE, the transient thickness profile of a draining thin liquid film was measured and modeled. The interfacial conditions were determined in situ by measuring the Hamaker constant. The ISE and IAI systems are compared.« less

Anisotropic dielectric properties of two-dimensional matrix in pseudo-spin ferroelectric system

NASA Astrophysics Data System (ADS)

Kim, Se-Hun

2016-10-01

The anisotropic dielectric properties of a two-dimensional (2D) ferroelectric system were studied using the statistical calculation of the pseudo-spin Ising Hamiltonian model. It is necessary to delay the time for measurements of the observable and the independence of the new spin configuration under Monte Carlo sampling, in which the thermal equilibrium state depends on the temperature and size of the system. The autocorrelation time constants of the normalized relaxation function were determined by taking temperature and 2D lattice size into account. We discuss the dielectric constants of a two-dimensional ferroelectric system by using the Metropolis method in view of the Slater-Takagi defect energies.

Deep neural networks for direct, featureless learning through observation: The case of two-dimensional spin models

NASA Astrophysics Data System (ADS)

Mills, Kyle; Tamblyn, Isaac

2018-03-01

We demonstrate the capability of a convolutional deep neural network in predicting the nearest-neighbor energy of the 4 ×4 Ising model. Using its success at this task, we motivate the study of the larger 8 ×8 Ising model, showing that the deep neural network can learn the nearest-neighbor Ising Hamiltonian after only seeing a vanishingly small fraction of configuration space. Additionally, we show that the neural network has learned both the energy and magnetization operators with sufficient accuracy to replicate the low-temperature Ising phase transition. We then demonstrate the ability of the neural network to learn other spin models, teaching the convolutional deep neural network to accurately predict the long-range interaction of a screened Coulomb Hamiltonian, a sinusoidally attenuated screened Coulomb Hamiltonian, and a modified Potts model Hamiltonian. In the case of the long-range interaction, we demonstrate the ability of the neural network to recover the phase transition with equivalent accuracy to the numerically exact method. Furthermore, in the case of the long-range interaction, the benefits of the neural network become apparent; it is able to make predictions with a high degree of accuracy, and do so 1600 times faster than a CUDA-optimized exact calculation. Additionally, we demonstrate how the neural network succeeds at these tasks by looking at the weights learned in a simplified demonstration.

Simulation of magnetoelastic response of iron nanowire loop

NASA Astrophysics Data System (ADS)

Huang, Junping; Peng, Xianghe; Wang, Zhongchang; Hu, Xianzhi

2018-03-01

We analyzed the magnetoelastic responses of one-dimensional iron nanowire loop systems with quantum statistical mechanics, treating the particles in the systems as identical bosons with an arbitrary integer spin. Under the assumptions adopted, we demonstrated that the Hamiltonian of the system can be separated into two parts, corresponding to two Ising subsystems, describing the particle spin and the particle displacement, respectively. Because the energy of the particle motion at atomic scale is quantized, there should be more the strict constraint on the particle displacement Ising subsystem. Making use of the existing results for Ising system, the partition function of the system was derived into two parts, corresponding respectively to the two Ising subsystems. Then the Gibbs distribution was obtained by statistical mechanics, and the description for the magnetoelastic response was derived. The magnetoelastic responses were predicted with the developed approach, and the comparison with the results calculated with VASP demonstrates the validity of the developed approach.

On the mixing time in the Wang-Landau algorithm

NASA Astrophysics Data System (ADS)

Fadeeva, Marina; Shchur, Lev

2018-01-01

We present preliminary results of the investigation of the properties of the Markov random walk in the energy space generated by the Wang-Landau probability. We build transition matrix in the energy space (TMES) using the exact density of states for one-dimensional and two-dimensional Ising models. The spectral gap of TMES is inversely proportional to the mixing time of the Markov chain. We estimate numerically the dependence of the mixing time on the lattice size, and extract the mixing exponent.

Correction to verdonck and tuerlinckx (2014).

PubMed

2015-01-01

Reports an error in "The Ising Decision Maker: A binary stochastic network for choice response time" by Stijn Verdonck and Francis Tuerlinckx (Psychological Review, 2014[Jul], Vol 121[3], 422-462). An inaccurate assumption in Appendix B (provided in the erratum) led to an oversimplified result in Equation 18 (the diffusion equations associated with the microscopically defined dynamics). The authors sincerely thank Rani Moran for making them aware of the problem. Only the expression of the diffusion coefficient D is incorrect, and should be changed, as indicated in the erratum. Both the cause of the problem and the solution are also explained in the erratum. (The following abstract of the original article appeared in record 2014-31650-006.) The Ising Decision Maker (IDM) is a new formal model for speeded two-choice decision making derived from the stochastic Hopfield network or dynamic Ising model. On a microscopic level, it consists of 2 pools of binary stochastic neurons with pairwise interactions. Inside each pool, neurons excite each other, whereas between pools, neurons inhibit each other. The perceptual input is represented by an external excitatory field. Using methods from statistical mechanics, the high-dimensional network of neurons (microscopic level) is reduced to a two-dimensional stochastic process, describing the evolution of the mean neural activity per pool (macroscopic level). The IDM can be seen as an abstract, analytically tractable multiple attractor network model of information accumulation. In this article, the properties of the IDM are studied, the relations to existing models are discussed, and it is shown that the most important basic aspects of two-choice response time data can be reproduced. In addition, the IDM is shown to predict a variety of observed psychophysical relations such as Piéron's law, the van der Molen-Keuss effect, and Weber's law. Using Bayesian methods, the model is fitted to both simulated and real data, and its performance is compared to the Ratcliff diffusion model. (PsycINFO Database Record (c) 2015 APA, all rights reserved).

Markov chain sampling of the O(n) loop models on the infinite plane

NASA Astrophysics Data System (ADS)

Herdeiro, Victor

2017-07-01

A numerical method was recently proposed in Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016), 10.1103/PhysRevE.94.043322] showing a precise sampling of the infinite plane two-dimensional critical Ising model for finite lattice subsections. The present note extends the method to a larger class of models, namely the O(n) loop gas models for n ∈(1 ,2 ] . We argue that even though the Gibbs measure is nonlocal, it is factorizable on finite subsections when sufficient information on the loops touching the boundaries is stored. Our results attempt to show that provided an efficient Markov chain mixing algorithm and an improved discrete lattice dilation procedure the planar limit of the O(n) models can be numerically studied with efficiency similar to the Ising case. This confirms that scale invariance is the only requirement for the present numerical method to work.

Ising tricriticality in the extended Hubbard model with bond dimerization

NASA Astrophysics Data System (ADS)

Fehske, Holger; Ejima, Satoshi; Lange, Florian; Essler, Fabian H. L.

We explore the quantum phase transition between Peierls and charge-density-wave insulating states in the one-dimensional, half-filled, extended Hubbard model with explicit bond dimerization. We show that the critical line of the continuous Ising transition terminates at a tricritical point, belonging to the universality class of the tricritical Ising model with central charge c=7/10. Above this point, the quantum phase transition becomes first order. Employing a numerical matrix-product-state based (infinite) density-matrix renormalization group method we determine the ground-state phase diagram, the spin and two-particle charge excitations gaps, and the entanglement properties of the model with high precision. Performing a bosonization analysis we can derive a field description of the transition region in terms of a triple sine-Gordon model. This allows us to derive field theory predictions for the power-law (exponential) decay of the density-density (spin-spin) and bond-order-wave correlation functions, which are found to be in excellent agreement with our numerical results. This work was supported by Deutsche Forschungsgemeinschaft (Germany), SFB 652, project B5, and by the EPSRC under Grant No. EP/N01930X/1 (FHLE).

Dynamical transitions of a driven Ising interface

NASA Astrophysics Data System (ADS)

Sahai, Manish K.; Sengupta, Surajit

2008-03-01

We study the structure of an interface in a three-dimensional Ising system created by an external nonuniform field H(r,t) . H changes sign over a two-dimensional plane of arbitrary orientation. When the field is pulled with velocity ve , [i.e., H(r,t)=H(r-vet) ], the interface undergoes several dynamical transitions. For low velocities it is pinned by the field profile and moves along with it, the distribution of local slopes undergoing a series of commensurate-incommensurate transitions. For large ve the interface depins and grows with Kardar-Parisi-Zhang exponents.

Critical behavior of the extended Hubbard model with bond dimerization

NASA Astrophysics Data System (ADS)

Ejima, Satoshi; Lange, Florian; Essler, Fabian H. L.; Fehske, Holger

2018-05-01

Exploiting the matrix-product-state based density-matrix renormalization group (DMRG) technique we study the one-dimensional extended (U-V) Hubbard model with explicit bond dimerization in the half-filled band sector. In particular we investigate the nature of the quantum phase transition, taking place with growing ratio V / U between the symmetry-protected-topological and charge-density-wave insulating states. The (weak-coupling) critical line of continuous Ising transitions with central charge c = 1 / 2 terminates at a tricritical point belonging to the universality class of the dilute Ising model with c = 7 / 10 . We demonstrate that our DMRG data perfectly match with (tricritical) Ising exponents, e.g., for the order parameter β = 1 / 8 (1/24) and correlation length ν = 1 (5/9). Beyond the tricritical Ising point, in the strong-coupling regime, the quantum phase transition becomes first order.

Mixed-order phase transition in a one-dimensional model.

PubMed

Bar, Amir; Mukamel, David

2014-01-10

We introduce and analyze an exactly soluble one-dimensional Ising model with long range interactions that exhibits a mixed-order transition, namely a phase transition in which the order parameter is discontinuous as in first order transitions while the correlation length diverges as in second order transitions. Such transitions are known to appear in a diverse classes of models that are seemingly unrelated. The model we present serves as a link between two classes of models that exhibit a mixed-order transition in one dimension, namely, spin models with a coupling constant that decays as the inverse distance squared and models of depinning transitions, thus making a step towards a unifying framework.

Two-dimensional RCFT's without Kac-Moody symmetry

NASA Astrophysics Data System (ADS)

Hampapura, Harsha R.; Mukhi, Sunil

2016-07-01

Using the method of modular-invariant differential equations, we classify a family of Rational Conformal Field Theories with two and three characters having no Kac-Moody algebra. In addition to unitary and non-unitary minimal models, we find "dual" theories whose characters obey bilinear relations with those of the minimal models to give the Moonshine Module. In some ways this relation is analogous to cosets of meromorphic CFT's. The theory dual in this sense to the Ising model has central charge 47/2 and is related to the Baby Monster Module.

Bifurcation analysis and phase diagram of a spin-string model with buckled states.

PubMed

Ruiz-Garcia, M; Bonilla, L L; Prados, A

2017-12-01

We analyze a one-dimensional spin-string model, in which string oscillators are linearly coupled to their two nearest neighbors and to Ising spins representing internal degrees of freedom. String-spin coupling induces a long-range ferromagnetic interaction among spins that competes with a spin-spin antiferromagnetic coupling. As a consequence, the complex phase diagram of the system exhibits different flat rippled and buckled states, with first or second order transition lines between states. This complexity translates to the two-dimensional version of the model, whose numerical solution has been recently used to explain qualitatively the rippled to buckled transition observed in scanning tunneling microscopy experiments with suspended graphene sheets. Here we describe in detail the phase diagram of the simpler one-dimensional model and phase stability using bifurcation theory. This gives additional insight into the physical mechanisms underlying the different phases and the behavior observed in experiments.

Bifurcation analysis and phase diagram of a spin-string model with buckled states

NASA Astrophysics Data System (ADS)

Ruiz-Garcia, M.; Bonilla, L. L.; Prados, A.

2017-12-01

We analyze a one-dimensional spin-string model, in which string oscillators are linearly coupled to their two nearest neighbors and to Ising spins representing internal degrees of freedom. String-spin coupling induces a long-range ferromagnetic interaction among spins that competes with a spin-spin antiferromagnetic coupling. As a consequence, the complex phase diagram of the system exhibits different flat rippled and buckled states, with first or second order transition lines between states. This complexity translates to the two-dimensional version of the model, whose numerical solution has been recently used to explain qualitatively the rippled to buckled transition observed in scanning tunneling microscopy experiments with suspended graphene sheets. Here we describe in detail the phase diagram of the simpler one-dimensional model and phase stability using bifurcation theory. This gives additional insight into the physical mechanisms underlying the different phases and the behavior observed in experiments.

Classical simulation of infinite-size quantum lattice systems in two spatial dimensions.

PubMed

Jordan, J; Orús, R; Vidal, G; Verstraete, F; Cirac, J I

2008-12-19

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)10.1103/PhysRevLett.98.070201]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.

Critical behavior of the quantum spin- {1}/{2} anisotropic Heisenberg model

NASA Astrophysics Data System (ADS)

Sousa, J. Ricardo de

A two-step renormalization group approach - a decimation followed by an effective field renormalization group (EFRG) - is proposed in this work to study the critical behavior of the quantum spin- {1}/{2} anisotropic Heisenberg model. The new method is illustrated by employing approximations in which clusters with one, two and three spins are used. The values of the critical parameter and critical exponent, in two- and three-dimensional lattices, for the Ising and isotropic Heisenberg limits are calculated and compared with other renormalization group approaches and exact (or series) results.

Testing ground for fluctuation theorems: The one-dimensional Ising model

NASA Astrophysics Data System (ADS)

Lemos, C. G. O.; Santos, M.; Ferreira, A. L.; Figueiredo, W.

2018-04-01

In this paper we determine the nonequilibrium magnetic work performed on a Ising model and relate it to the fluctuation theorem derived some years ago by Jarzynski. The basic idea behind this theorem is the relationship connecting the free energy difference between two thermodynamic states of a system and the average work performed by an external agent, in a finite time, through nonequilibrium paths between the same thermodynamic states. We test the validity of this theorem by considering the one-dimensional Ising model where the free energy is exactly determined as a function of temperature and magnetic field. We have found that the Jarzynski theorem remains valid for all the values of the rate of variation of the magnetic field applied to the system. We have also determined the probability distribution function for the work performed on the system for the forward and reverse processes and verified that predictions based on the Crooks relation are equally correct. We also propose a method to calculate the lag between the current state of the system and that of the equilibrium based on macroscopic variables. We have shown that the lag increases with the sweeping rate of the field at its final value for the reverse process, while it decreases in the case of the forward process. The lag increases linearly with the size of the chain and with a slope decreasing with the inverse of the rate of variation of the field.

Special course for Masters and PhD students: phase transitions, Landau theory, 1D Ising model, the dimension of the space and Cosmology

NASA Astrophysics Data System (ADS)

Udodov, Vladimir; Katanov Khakas State Univ Team

2014-03-01

Symmetry breaking transitions. The phenomenological (L.D.Landau, USSR, 1937) way to describe phase transitions (PT's). Order parameter and loss of the symmetry. The second derivative of the free energy changes jump wise at the transition, i.e. we have a mathematical singularity and second order PT (TC>0). Extremes of free energy. A point of loss of stability of the symmetrical phase. The eigenfrequency of PT and soft mode behavior. The conditions of applicability of the Landau theory (A.Levanyuk, 1959, V.Ginzburg, 1960). 1D Ising model and exact solution by a transfer matrix method. Critical exponents in the L.Landau PT's theory and for 1D Ising model. Scaling hypothesis (1965) for 1D Ising model with zero critical temperature. The order of PT in 1D Ising model in the framework of the R.Baxter approach. The anthropic principle and the dimension of the space. Why do we have a three-dimensional space? Big bang, the cosmic vacuum, inflation and PT's. Higgs boson and symmetry breaking transitions. Author acknowledges the support of Katanov Khakas State University.

Ecological risk assessment of TBT in Ise Bay.

PubMed

Yamamoto, Joji; Yonezawa, Yoshitaka; Nakata, Kisaburo; Horiguchi, Fumio

2009-02-01

An ecological risk assessment of tributyltin (TBT) in Ise Bay was conducted using the margin of exposure (MOE) method. The assessment endpoint was defined to protect the survival, growth and reproduction of marine organisms. Sources of TBT in this study were assumed to be commercial vessels in harbors and navigation routes. Concentrations of TBT in Ise Bay were estimated using a three-dimensional hydrodynamic model, an ecosystem model and a chemical fate model. Estimated MOEs for marine organisms for 1990 and 2008 were approximately 0.1-2.0 and over 100 respectively, indicating a declining temporal trend in the probability of adverse effects. The chemical fate model predicts a much longer persistence of TBT in sediments than in the water column. Therefore, it is necessary to monitor the harmful effects of TBT on benthic organisms.

Surface critical behavior of thin Ising films at the ‘special point’

NASA Astrophysics Data System (ADS)

Moussa, Najem; Bekhechi, Smaine

2003-03-01

The critical surface phenomena of a magnetic thin Ising film is studied using numerical Monte-Carlo method based on Wolff cluster algorithm. With varying the surface coupling, js= Js/ J, the phase diagram exhibits a special surface coupling jsp at which all the films have a unique critical temperature Tc for an arbitrary thickness n. In spite of this, the critical exponent of the surface magnetization at the special point is found to increase with n. Moreover, non-universal features as well as dimensionality crossover from two- to three-dimensional behavior are found at this point.

Thermodynamics of alternating spin chains with competing nearest- and next-nearest-neighbor interactions: Ising model

NASA Astrophysics Data System (ADS)

Pini, Maria Gloria; Rettori, Angelo

1993-08-01

The thermodynamical properties of an alternating spin (S,s) one-dimensional (1D) Ising model with competing nearest- and next-nearest-neighbor interactions are exactly calculated using a transfer-matrix technique. In contrast to the case S=s=1/2, previously investigated by Harada, the alternation of different spins (S≠s) along the chain is found to give rise to two-peaked static structure factors, signaling the coexistence of different short-range-order configurations. The relevance of our calculations with regard to recent experimental data by Gatteschi et al. in quasi-1D molecular magnetic materials, R (hfac)3 NITEt (R=Gd, Tb, Dy, Ho, Er, . . .), is discussed; hfac is hexafluoro-acetylacetonate and NlTEt is 2-Ethyl-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-1-oxyl-3-oxide.

Magnetic and thermodynamic properties of Ising model with borophene structure in a longitudinal magnetic field

NASA Astrophysics Data System (ADS)

Shi, Kaile; Jiang, Wei; Guo, Anbang; Wang, Kai; Wu, Chuang

2018-06-01

The magnetic and thermodynamic properties of borophene structure have been studied for the first time by Monte Carlo simulation. Two-dimensional borophene structure consisting of seven hexagonal B36 units is described by Ising model. Each B36 basic unit includes three benzene-like with spin-3/2. The general formula for the borophene structure is given. The numerical results of the magnetization, the magnetic susceptibility, the internal energy and the specific heat are studied with various parameters. The possibility to test the predicted magnetism in experiment are illustrated, for instance, the maximum on the magnetization curve. The multiple hysteresis loops and the magnetization plateaus are sensitive to the ferromagnetic or ferrimagnetic exchange coupling in borophene structure. The results show the borophene structure could have applications in spintronics, which deserves further studies in experiments.

Bethe ansatz for two-magnon scattering states in 2D and 3D Heisenberg–Ising ferromagnets

NASA Astrophysics Data System (ADS)

Bibikov, P. N.

2018-04-01

Two different versions of Bethe ansatz are suggested for evaluation of scattering two-magnon states in 2D and 3D Heisenberg–Ising ferromagnets on square and simple cubic lattices. It is shown that the two-magnon sector is subdivided on two subsectors related to non-interacting and scattering magnons. The former subsector possess an integrable regular dynamics and may be described by a natural modification of the usual Bethe Ansatz. The latter one is characterized by a non-integrable chaotic dynamics and may be treated only within discrete degenerative version of Bethe Ansatz previously suggested by the author. Some of these results are generalized for multi-magnon states of the Heisenberg–Ising ferromagnet on a D dimensional hyper cubic lattice. Dedicated to the memory of L D Faddeev.

Critical and Griffiths-McCoy singularities in quantum Ising spin glasses on d-dimensional hypercubic lattices: A series expansion study.

PubMed

Singh, R R P; Young, A P

2017-08-01

We study the ±J transverse-field Ising spin-glass model at zero temperature on d-dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d=6, which is below the upper critical dimension of d=8. In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.

Critical and Griffiths-McCoy singularities in quantum Ising spin glasses on d -dimensional hypercubic lattices: A series expansion study

NASA Astrophysics Data System (ADS)

Singh, R. R. P.; Young, A. P.

2017-08-01

We study the ±J transverse-field Ising spin-glass model at zero temperature on d -dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d =6 , which is below the upper critical dimension of d =8 . In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.

Freezing in stripe states for kinetic Ising models: a comparative study of three dynamics

NASA Astrophysics Data System (ADS)

Godrèche, Claude; Pleimling, Michel

2018-04-01

We present a comparative study of the fate of an Ising ferromagnet on the square lattice with periodic boundary conditions evolving under three different zero-temperature dynamics. The first one is Glauber dynamics, the two other dynamics correspond to two limits of the directed Ising model, defined by rules that break the full symmetry of the former, yet sharing the same Boltzmann-Gibbs distribution at stationarity. In one of these limits the directed Ising model is reversible, in the other one it is irreversible. For the kinetic Ising-Glauber model, several recent studies have demonstrated the role of critical percolation to predict the probabilities for the system to reach the ground state or to fall in a metastable state. We investigate to what extent the predictions coming from critical percolation still apply to the two other dynamics.

Comment on "Many-body localization in Ising models with random long-range interactions"

NASA Astrophysics Data System (ADS)

Maksymov, Andrii O.; Rahman, Noah; Kapit, Eliot; Burin, Alexander L.

2017-11-01

This Comment is dedicated to the investigation of many-body localization in a quantum Ising model with long-range power-law interactions r-α, relevant for a variety of systems ranging from electrons in Anderson insulators to spin excitations in chains of cold atoms. It has earlier been argued [arXiv:cond-mat/0611387 (2005); Phys. Rev. B 91, 094202 (2015), 10.1103/PhysRevB.91.094202] that this model obeys the dimensional constraint suggesting the delocalization of all finite-temperature states in the thermodynamic limit for α ≤2 d in a d -dimensional system. This expectation conflicts with the recent numerical studies of the specific interacting spin model of Li et al. [Phys. Rev. A 94, 063625 (2016), 10.1103/PhysRevA.94.063625]. To resolve this controversy we reexamine the model of Li et al. [Phys. Rev. A 94, 063625 (2016), 10.1103/PhysRevA.94.063625] and demonstrate that the infinite-temperature states there obey the dimensional constraint. The earlier developed scaling theory for the critical system size required for delocalization is extended to small exponents 0 ≤α ≤d . The disagreements between the two works are explained by the nonstandard selection of investigated states in the ordered phase in the work of Li et al. [Phys. Rev. A 94, 063625 (2016)10.1103/PhysRevA.94.063625].

On the p, q-binomial distribution and the Ising model

NASA Astrophysics Data System (ADS)

Lundow, P. H.; Rosengren, A.

2010-08-01

We employ p, q-binomial coefficients, a generalisation of the binomial coefficients, to describe the magnetisation distributions of the Ising model. For the complete graph this distribution corresponds exactly to the limit case p = q. We apply our investigation to the simple d-dimensional lattices for d = 1, 2, 3, 4, 5 and fit p, q-binomial distributions to our data, some of which are exact but most are sampled. For d = 1 and d = 5, the magnetisation distributions are remarkably well-fitted by p,q-binomial distributions. For d = 4 we are only slightly less successful, while for d = 2, 3 we see some deviations (with exceptions!) between the p, q-binomial and the Ising distribution. However, at certain temperatures near T c the statistical moments of the fitted distribution agree with the moments of the sampled data within the precision of sampling. We begin the paper by giving results of the behaviour of the p, q-distribution and its moment growth exponents given a certain parameterisation of p, q. Since the moment exponents are known for the Ising model (or at least approximately for d = 3) we can predict how p, q should behave and compare this to our measured p, q. The results speak in favour of the p, q-binomial distribution's correctness regarding its general behaviour in comparison to the Ising model. The full extent to which they correctly model the Ising distribution, however, is not settled.

Nonequilibrium Statistical Mechanics in One Dimension

NASA Astrophysics Data System (ADS)

Privman, Vladimir

2005-08-01

Part I. Reaction-Diffusion Systems and Models of Catalysis; 1. Scaling theories of diffusion-controlled and ballistically-controlled bimolecular reactions S. Redner; 2. The coalescence process, A+A->A, and the method of interparticle distribution functions D. ben-Avraham; 3. Critical phenomena at absorbing states R. Dickman; Part II. Kinetic Ising Models; 4. Kinetic ising models with competing dynamics: mappings, correlations, steady states, and phase transitions Z. Racz; 5. Glauber dynamics of the ising model N. Ito; 6. 1D Kinetic ising models at low temperatures - critical dynamics, domain growth, and freezing S. Cornell; Part III. Ordering, Coagulation, Phase Separation; 7. Phase-ordering dynamics in one dimension A. J. Bray; 8. Phase separation, cluster growth, and reaction kinetics in models with synchronous dynamics V. Privman; 9. Stochastic models of aggregation with injection H. Takayasu and M. Takayasu; Part IV. Random Sequential Adsorption and Relaxation Processes; 10. Random and cooperative sequential adsorption: exactly solvable problems on 1D lattices, continuum limits, and 2D extensions J. W. Evans; 11. Lattice models of irreversible adsorption and diffusion P. Nielaba; 12. Deposition-evaporation dynamics: jamming, conservation laws and dynamical diversity M. Barma; Part V. Fluctuations In Particle and Surface Systems; 13. Microscopic models of macroscopic shocks S. A. Janowsky and J. L. Lebowitz; 14. The asymmetric exclusion model: exact results through a matrix approach B. Derrida and M. R. Evans; 15. Nonequilibrium surface dynamics with volume conservation J. Krug; 16. Directed walks models of polymers and wetting J. Yeomans; Part VI. Diffusion and Transport In One Dimension; 17. Some recent exact solutions of the Fokker-Planck equation H. L. Frisch; 18. Random walks, resonance, and ratchets C. R. Doering and T. C. Elston; 19. One-dimensional random walks in random environment K. Ziegler; Part VII. Experimental Results; 20. Diffusion-limited exciton kinetics in one-dimensional systems R. Kroon and R. Sprik; 21. Experimental investigations of molecular and excitonic elementary reaction kinetics in one-dimensional systems R. Kopelman and A. L. Lin; 22. Luminescence quenching as a probe of particle distribution S. H. Bossmann and L. S. Schulman; Index.

Charge-patterning phase transition on a surface lattice of titratable sites adjacent to an electrolyte solution

NASA Astrophysics Data System (ADS)

Shore, Joel; Thurston, George

We discuss a model for a charge-patterning phase transition on a two-dimensional square lattice of titratable sites, here regarded as protonation sites, placed on a square lattice in a dielectric medium just below the planar interface between this medium and an aqueous salt solution. Within Debye-Huckel theory, the analytical form of the electrostatic repulsion between protonated sites exhibits an approximate inverse cubic power-law decrease beyond short distances. The problem can thus be mapped onto the two-dimensional antiferromagnetic Ising model with this longer-range interaction, which we study with Monte Carlo simulations. As we increase pH, the occupation probability of a site decreases from 1 at low pH to 0 at high pH. For sufficiently-strong interaction strengths, a phase transition occurs as the occupation probability of 1/2 is approached: the charges arrange themselves into a checkerboard pattern. This ordered phase persists over a range of pH until a transition occurs back to a disordered state. This state is the analogue of the Neel state in the antiferromagnetic Ising spin model. More complicated ordered phases are expected for sufficiently strong interactions (with occupation probabilities of 1/4 and 3/4) and if the lattice is triangular rather than square. This work was supported by NIH EY018249 (GMT).

Identifying differentially expressed genes in cancer patients using a non-parameter Ising model.

PubMed

Li, Xumeng; Feltus, Frank A; Sun, Xiaoqian; Wang, James Z; Luo, Feng

2011-10-01

Identification of genes and pathways involved in diseases and physiological conditions is a major task in systems biology. In this study, we developed a novel non-parameter Ising model to integrate protein-protein interaction network and microarray data for identifying differentially expressed (DE) genes. We also proposed a simulated annealing algorithm to find the optimal configuration of the Ising model. The Ising model was applied to two breast cancer microarray data sets. The results showed that more cancer-related DE sub-networks and genes were identified by the Ising model than those by the Markov random field model. Furthermore, cross-validation experiments showed that DE genes identified by Ising model can improve classification performance compared with DE genes identified by Markov random field model. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Critical space-time networks and geometric phase transitions from frustrated edge antiferromagnetism

NASA Astrophysics Data System (ADS)

Trugenberger, Carlo A.

2015-12-01

Recently I proposed a simple dynamical network model for discrete space-time that self-organizes as a graph with Hausdorff dimension dH=4 . The model has a geometric quantum phase transition with disorder parameter (dH-ds) , where ds is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean-field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions.

Spin flip statistics and spin wave interference patterns in Ising ferromagnetic films: A Monte Carlo study.

PubMed

Acharyya, Muktish

2017-07-01

The spin wave interference is studied in two dimensional Ising ferromagnet driven by two coherent spherical magnetic field waves by Monte Carlo simulation. The spin waves are found to propagate and interfere according to the classic rule of interference pattern generated by two point sources. The interference pattern of spin wave is observed in one boundary of the lattice. The interference pattern is detected and studied by spin flip statistics at high and low temperatures. The destructive interference is manifested as the large number of spin flips and vice versa.

Intraoperative 3D Navigation for Single or Multiple 125I-Seed Localization in Breast-Preserving Cancer Surgery.

PubMed

Pouw, Bas; de Wit-van der Veen, Linda J; van Duijnhoven, Frederieke; Rutgers, Emiel J Th; Stokkel, Marcel P M; Valdés Olmos, Renato A; Vrancken Peeters, Marie-Jeanne T F D

2016-05-01

Mammographic screening has led to the identification of more women with nonpalpable breast cancer, many of them to be treated with breast-preserving surgery. To accomplish radical tumor excision, adequate localization techniques such as radioactive seed localization (RSL) are required. For RSL, a radioactive I-seed is implanted central in the tumor to enable intraoperative localization using a γ-probe. In case of extensive tumor or multifocal carcinoma, multiple I-seeds can be used to delineate the involved area. Preoperative imaging is performed different from surgical positioning; therefore, exact I-seed depth remains unknown during surgery. Twenty patients (mean age, 56.8 years) with 25 implanted I-seeds scheduled for RSL were included. Sixteen patients had 1 I-seed implanted in the primary lesion, 3 patients had 2 I-seeds, and 1 patient had 3 I-seeds. Freehand SPECT localized I-seeds by measuring γ-counts from different directions, all registered by an optical tracking system. A reconstruction and visualization algorithm enabled 3-dimensional (3D) navigation toward the I-seeds. Freehand SPECT visualized all I-seeds in primary tumors and provided preincision depth information. The deviation, mean (SD), between the freehand SPECT depth and the surgical depth estimation was 1.9 (2.1) mm (range, 0-7 mm). Three-dimensional freehand SPECT was especially useful identifying multiple implanted I-seeds because the conventional γ-probe has more difficulty discriminating I-seeds transcutaneous. Freehand SPECT with 3D navigation is a valuable tool in RSL for both single and multiple implanted I-seeds in breast-preserving cancer surgery. Freehand SPECT provides continuous updating 3D imaging with information about depth and location of the I-seeds contributing to adequate excision of nonpalpable breast cancer.

CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm: 2D and 3D Ising, Potts, and XY models

NASA Astrophysics Data System (ADS)

Komura, Yukihiro; Okabe, Yutaka

2014-03-01

We present sample CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm. We deal with the classical spin models; the Ising model, the q-state Potts model, and the classical XY model. As for the lattice, both the 2D (square) lattice and the 3D (simple cubic) lattice are treated. We already reported the idea of the GPU implementation for 2D models (Komura and Okabe, 2012). We here explain the details of sample programs, and discuss the performance of the present GPU implementation for the 3D Ising and XY models. We also show the calculated results of the moment ratio for these models, and discuss phase transitions. Catalogue identifier: AERM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERM_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5632 No. of bytes in distributed program, including test data, etc.: 14688 Distribution format: tar.gz Programming language: C, CUDA. Computer: System with an NVIDIA CUDA enabled GPU. Operating system: System with an NVIDIA CUDA enabled GPU. Classification: 23. External routines: NVIDIA CUDA Toolkit 3.0 or newer Nature of problem: Monte Carlo simulation of classical spin systems. Ising, q-state Potts model, and the classical XY model are treated for both two-dimensional and three-dimensional lattices. Solution method: GPU-based Swendsen-Wang multi-cluster spin flip Monte Carlo method. The CUDA implementation for the cluster-labeling is based on the work by Hawick et al. [1] and that by Kalentev et al. [2]. Restrictions: The system size is limited depending on the memory of a GPU. Running time: For the parameters used in the sample programs, it takes about a minute for each program. Of course, it depends on the system size, the number of Monte Carlo steps, etc. References: [1] K.A. Hawick, A. Leist, and D. P. Playne, Parallel Computing 36 (2010) 655-678 [2] O. Kalentev, A. Rai, S. Kemnitzb, and R. Schneider, J. Parallel Distrib. Comput. 71 (2011) 615-620

Wang-Landau method for calculating Rényi entropies in finite-temperature quantum Monte Carlo simulations.

PubMed

Inglis, Stephen; Melko, Roger G

2013-01-01

We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) simulations for the purpose of calculating the Rényi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analog to the density of states for stochastic series expansion QMC, allowing a direct calculation of Rényi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, a 2D transverse field Ising model, and a three-dimensional Heisenberg model, confirming a critical scaling of the mutual information in cases with a finite-temperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.

Crystal structure and partial Ising-like magnetic ordering of orthorhombic D y 2 Ti O 5

DOE PAGES

Shamblin, Jacob; Calder, Stuart; Dun, Zhiling; ...

2016-07-12

The structure and magnetic properties of orthorhombic Dy 2TiO 5 have been investigated using x-ray diffraction, neutron diffraction, and alternating current (ac)/direct current (dc) magnetic susceptibility measurements. In this paper, we report a continuous structural distortion below 100 K characterized by negative thermal expansion in the [0 1 0] direction. Neutron diffraction and magnetic susceptibility measurements revealed that two-dimensional (2D) magnetic ordering begins at 3.1 K, which is followed by a three-dimensional magnetic transition at 1.7 K. The magnetic structure has been solved through a representational analysis approach and can be indexed with the propagation vector k = [0 1/2more » 0]. The spin structure corresponds to a coplanar model of interwoven 2D “sheets” extending in the [0 1 0] direction. The local crystal field is different for each Dy 3+ ion (Dy1 and Dy2), one of which possesses strong uniaxial symmetry indicative of Ising-like magnetic ordering. In conclusion, consequently, two succeeding transitions under magnetic field are observed in the ac susceptibility, which are associated with flipping each Dy 3+ spin independently.« less

Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models

NASA Astrophysics Data System (ADS)

Labuhn, Henning; Barredo, Daniel; Ravets, Sylvain; de Léséleuc, Sylvain; Macrì, Tommaso; Lahaye, Thierry; Browaeys, Antoine

2016-06-01

Spin models are the prime example of simplified many-body Hamiltonians used to model complex, strongly correlated real-world materials. However, despite the simplified character of such models, their dynamics often cannot be simulated exactly on classical computers when the number of particles exceeds a few tens. For this reason, quantum simulation of spin Hamiltonians using the tools of atomic and molecular physics has become a very active field over the past years, using ultracold atoms or molecules in optical lattices, or trapped ions. All of these approaches have their own strengths and limitations. Here we report an alternative platform for the study of spin systems, using individual atoms trapped in tunable two-dimensional arrays of optical microtraps with arbitrary geometries, where filling fractions range from 60 to 100 per cent. When excited to high-energy Rydberg D states, the atoms undergo strong interactions whose anisotropic character opens the way to simulating exotic matter. We illustrate the versatility of our system by studying the dynamics of a quantum Ising-like spin-1/2 system in a transverse field with up to 30 spins, for a variety of geometries in one and two dimensions, and for a wide range of interaction strengths. For geometries where the anisotropy is expected to have small effects on the dynamics, we find excellent agreement with ab initio simulations of the spin-1/2 system, while for strongly anisotropic situations the multilevel structure of the D states has a measurable influence. Our findings establish arrays of single Rydberg atoms as a versatile platform for the study of quantum magnetism.

Interplay of interfacial noise and curvature-driven dynamics in two dimensions

NASA Astrophysics Data System (ADS)

Roy, Parna; Sen, Parongama

2017-02-01

We explore the effect of interplay of interfacial noise and curvature-driven dynamics in a binary spin system. An appropriate model is the generalized two-dimensional voter model proposed earlier [M. J. de Oliveira, J. F. F. Mendes, and M. A. Santos, J. Phys. A: Math. Gen. 26, 2317 (1993), 10.1088/0305-4470/26/10/006], where the flipping probability of a spin depends on the state of its neighbors and is given in terms of two parameters, x and y . x =0.5 andy =1 correspond to the conventional voter model which is purely interfacial noise driven, while x =1 and y =1 correspond to the Ising model, where coarsening is fully curvature driven. The coarsening phenomena for 0.5 0.5 ; the effect of x appears in altering the value of the parameter occurring in the scaling function only.

Self-dual random-plaquette gauge model and the quantum toric code

NASA Astrophysics Data System (ADS)

Takeda, Koujin; Nishimori, Hidetoshi

2004-05-01

We study the four-dimensional Z2 random-plaquette lattice gauge theory as a model of topological quantum memory, the toric code in particular. In this model, the procedure of quantum error correction works properly in the ordered (Higgs) phase, and phase boundary between the ordered (Higgs) and disordered (confinement) phases gives the accuracy threshold of error correction. Using self-duality of the model in conjunction with the replica method, we show that this model has exactly the same mathematical structure as that of the two-dimensional random-bond Ising model, which has been studied very extensively. This observation enables us to derive a conjecture on the exact location of the multicritical point (accuracy threshold) of the model, pc=0.889972…, and leads to several nontrivial results including bounds on the accuracy threshold in three dimensions.

Quantum phase transitions and decoupling of magnetic sublattices in the quasi-two-dimensional Ising magnet Co 3V 2O 8 in a transverse magnetic field

DOE PAGES

Fritsch, Katharina; Ehlers, G.; Rule, K. C.; ...

2015-11-05

We study the application of a magnetic field transverse to the easy axis, Ising direction in the quasi-two-dimensional kagome staircase magnet, Co 3V 2O 8, induces three quantum phase transitions at low temperatures, ultimately producing a novel high field polarized state, with two distinct sublattices. New time-of-flight neutron scattering techniques, accompanied by large angular access, high magnetic field infrastructure allow the mapping of a sequence of ferromagnetic and incommensurate phases and their accompanying spin excitations. Also, at least one of the transitions to incommensurate phases at μ 0H c1~6.25 T and μ 0H c2~7 T is discontinuous, while the finalmore » quantum critical point at μ 0H c3~13 T is continuous.« less

Analysis of the phase transition in the two-dimensional Ising ferromagnet using a Lempel-Ziv string-parsing scheme and black-box data-compression utilities

NASA Astrophysics Data System (ADS)

Melchert, O.; Hartmann, A. K.

2015-02-01

In this work we consider information-theoretic observables to analyze short symbolic sequences, comprising time series that represent the orientation of a single spin in a two-dimensional (2D) Ising ferromagnet on a square lattice of size L2=1282 for different system temperatures T . The latter were chosen from an interval enclosing the critical point Tc of the model. At small temperatures the sequences are thus very regular; at high temperatures they are maximally random. In the vicinity of the critical point, nontrivial, long-range correlations appear. Here we implement estimators for the entropy rate, excess entropy (i.e., "complexity"), and multi-information. First, we implement a Lempel-Ziv string-parsing scheme, providing seemingly elaborate entropy rate and multi-information estimates and an approximate estimator for the excess entropy. Furthermore, we apply easy-to-use black-box data-compression utilities, providing approximate estimators only. For comparison and to yield results for benchmarking purposes, we implement the information-theoretic observables also based on the well-established M -block Shannon entropy, which is more tedious to apply compared to the first two "algorithmic" entropy estimation procedures. To test how well one can exploit the potential of such data-compression techniques, we aim at detecting the critical point of the 2D Ising ferromagnet. Among the above observables, the multi-information, which is known to exhibit an isolated peak at the critical point, is very easy to replicate by means of both efficient algorithmic entropy estimation procedures. Finally, we assess how good the various algorithmic entropy estimates compare to the more conventional block entropy estimates and illustrate a simple modification that yields enhanced results.

Aging in the three-dimensional random-field Ising model

NASA Astrophysics Data System (ADS)

von Ohr, Sebastian; Manssen, Markus; Hartmann, Alexander K.

2017-07-01

We studied the nonequilibrium aging behavior of the random-field Ising model in three dimensions for various values of the disorder strength. This allowed us to investigate how the aging behavior changes across the ferromagnetic-paramagnetic phase transition. We investigated a large system size of N =2563 spins and up to 108 Monte Carlo sweeps. To reach these necessary long simulation times, we employed an implementation running on Intel Xeon Phi coprocessors, reaching single-spin-flip times as short as 6 ps. We measured typical correlation functions in space and time to extract a growing length scale and corresponding exponents.

Localization in a random XY model with long-range interactions: Intermediate case between single-particle and many-body problems

NASA Astrophysics Data System (ADS)

Burin, Alexander L.

2015-09-01

Many-body localization in an XY model with a long-range interaction is investigated. We show that in the regime of a high strength of disordering compared to the interaction an off-resonant flip-flop spin-spin interaction (hopping) generates the effective Ising interactions of spins in the third order of perturbation theory in a hopping. The combination of hopping and induced Ising interactions for the power-law distance dependent hopping V (R ) ∝R-α always leads to the localization breakdown in a thermodynamic limit of an infinite system at α <3 d /2 where d is a system dimension. The delocalization takes place due to the induced Ising interactions U (R ) ∝R-2 α of "extended" resonant pairs. This prediction is consistent with the numerical finite size scaling in one-dimensional systems. Many-body localization in an XY model is more stable with respect to the long-range interaction compared to a many-body problem with similar Ising and Heisenberg interactions requiring α ≥2 d which makes the practical implementations of this model more attractive for quantum information applications. The full summary of dimension constraints and localization threshold size dependencies for many-body localization in the case of combined Ising and hopping interactions is obtained using this and previous work and it is the subject for the future experimental verification using cold atomic systems.

Equilibrium and nonequilibrium models on Solomon networks

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2016-05-01

We investigate the critical properties of the equilibrium and nonequilibrium systems on Solomon networks. The equilibrium and nonequilibrium systems studied here are the Ising and Majority-vote models, respectively. These systems are simulated by applying the Monte Carlo method. We calculate the critical points, as well as the critical exponents ratio γ/ν, β/ν and 1/ν. We find that both systems present identical exponents on Solomon networks and are of different universality class as the regular two-dimensional ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

Finite-temperature spin dynamics in a perturbed quantum critical Ising chain with an E₈ symmetry.

PubMed

Wu, Jianda; Kormos, Márton; Si, Qimiao

2014-12-12

A spectrum exhibiting E₈ symmetry is expected to arise when a small longitudinal field is introduced in the transverse-field Ising chain at its quantum critical point. Evidence for this spectrum has recently come from neutron scattering measurements in cobalt niobate, a quasi-one-dimensional Ising ferromagnet. Unlike its zero-temperature counterpart, the finite-temperature dynamics of the model has not yet been determined. We study the dynamical spin structure factor of the model at low frequencies and nonzero temperatures, using the form factor method. Its frequency dependence is singular, but differs from the diffusion form. The temperature dependence of the nuclear magnetic resonance (NMR) relaxation rate has an activated form, whose prefactor we also determine. We propose NMR experiments as a means to further test the applicability of the E₈ description for CoNb₂O₆.

Quantum quench in an atomic one-dimensional Ising chain.

PubMed

Meinert, F; Mark, M J; Kirilov, E; Lauber, K; Weinmann, P; Daley, A J; Nägerl, H-C

2013-08-02

We study nonequilibrium dynamics for an ensemble of tilted one-dimensional atomic Bose-Hubbard chains after a sudden quench to the vicinity of the transition point of the Ising paramagnetic to antiferromagnetic quantum phase transition. The quench results in coherent oscillations for the orientation of effective Ising spins, detected via oscillations in the number of doubly occupied lattice sites. We characterize the quench by varying the system parameters. We report significant modification of the tunneling rate induced by interactions and show clear evidence for collective effects in the oscillatory response.

Equilibrium and nonequilibrium models on solomon networks with two square lattices

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

We investigate the critical properties of the equilibrium and nonequilibrium two-dimensional (2D) systems on Solomon networks with both nearest and random neighbors. The equilibrium and nonequilibrium 2D systems studied here by Monte Carlo simulations are the Ising and Majority-vote 2D models, respectively. We calculate the critical points as well as the critical exponent ratios γ/ν, β/ν, and 1/ν. We find that numerically both systems present the same exponents on Solomon networks (2D) and are of different universality class than the regular 2D ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

Coherent-Anomaly Method in Critical Phenomena. III. Mean-Field Transfer-Matrix Method in the 2D Ising Model

NASA Astrophysics Data System (ADS)

Hu, Xiao; Katori, Makoto; Suzuki, Masuo

1987-11-01

Two kinds of systematic mean-field transfer-matrix methods are formulated in the 2-dimensional Ising spin system, by introducing Weiss-like and Bethe-like approximations. All the critical exponents as well as the true critical point can be estimated in these methods following the CAM procedure. The numerical results of the above system are Tc*≃2.271 (J/kB), γ{=}γ'≃1.749, β≃0.131 and δ≃15.1. The specific heat is confirmd to be continuous and to have a logarithmic divergence at the true critical point, i.e., α{=}α'{=}0. Thus, the finite-degree-of-approximation scaling ansatz is shown to be correct and very powerful in practical estimations of the critical exponents as well as the true critical point.

The initial subevent of the 1994 Northridge, California, earthquake: Is earthquake size predictable?

USGS Publications Warehouse

Kilb, Debi; Gomberg, J.

1999-01-01

We examine the initial subevent (ISE) of the M?? 6.7, 1994 Northridge, California, earthquake in order to discriminate between two end-member rupture initiation models: the 'preslip' and 'cascade' models. Final earthquake size may be predictable from an ISE's seismic signature in the preslip model but not in the cascade model. In the cascade model ISEs are simply small earthquakes that can be described as purely dynamic ruptures. In this model a large earthquake is triggered by smaller earthquakes; there is no size scaling between triggering and triggered events and a variety of stress transfer mechanisms are possible. Alternatively, in the preslip model, a large earthquake nucleates as an aseismically slipping patch in which the patch dimension grows and scales with the earthquake's ultimate size; the byproduct of this loading process is the ISE. In this model, the duration of the ISE signal scales with the ultimate size of the earthquake, suggesting that nucleation and earthquake size are determined by a more predictable, measurable, and organized process. To distinguish between these two end-member models we use short period seismograms recorded by the Southern California Seismic Network. We address questions regarding the similarity in hypocenter locations and focal mechanisms of the ISE and the mainshock. We also compare the ISE's waveform characteristics to those of small earthquakes and to the beginnings of earthquakes with a range of magnitudes. We find that the focal mechanisms of the ISE and mainshock are indistinguishable, and both events may have nucleated on and ruptured the same fault plane. These results satisfy the requirements for both models and thus do not discriminate between them. However, further tests show the ISE's waveform characteristics are similar to those of typical small earthquakes in the vicinity and more importantly, do not scale with the mainshock magnitude. These results are more consistent with the cascade model.

Comparison of the ferromagnetic Blume-Emery-Griffiths model and the AF spin-1 longitudinal Ising model at low temperature

NASA Astrophysics Data System (ADS)

Thomaz, M. T.; Corrêa Silva, E. V.

2016-03-01

We derive the exact Helmholtz free energy (HFE) of the standard and staggered one-dimensional Blume-Emery-Griffiths (BEG) model in the presence of an external longitudinal magnetic field. We discuss in detail the thermodynamic behavior of the ferromagnetic version of the model, which exhibits magnetic field-dependent plateaux in the z-component of its magnetization at low temperatures. We also study the behavior of its specific heat and entropy, both per site, at finite temperature. The degeneracy of the ground state, at T=0, along the lines that separate distinct phases in the phase diagram of the ferromagnetic BEG model is calculated, extending the study of the phase diagram of the spin-1 antiferromagnetic (AF) Ising model in S.M. de Souza and M.T. Thomaz, J. Magn. and Magn. Mater. 354 (2014) 205 [5]. We explore the implications of the equality of phase diagrams, at T=0, of the ferromagnetic BEG model with K/|J| = - 2 and of the spin-1 AF Ising model for D/|J| > 1/2.

Ising Criticality of the Clock Model from Density of States Obtained by the Replica Exchange-Wang-Landau Method

NASA Astrophysics Data System (ADS)

Cadilhe, Antonio

2018-04-01

We performed extensive simulations, using the Replica Exchange-Wang-Landau method, of the clock model for orders 3 and 4 on a square lattice, where critical behaviors are expected to belong to the Ising universality class. Though order 2 represents the Ising model, thus, being exactly solvable in two-dimensions, we still provide such results for comparison to the other two orders. Results for various energy related quantities such as the mean energy per spin, specific heat, as well as logarithm scaling of the peak of the specific heat are presented and shown to follow Ising behavior. Additionally, we also present results related to magnetic quantities, such as the magnetization, magnetic susceptibility, and corresponding scaling behavior of the peak of the magnetic susceptibility. Again, our results show scaling in conformity to Ising critical behavior.

Disorder from order among anisotropic next-nearest-neighbor Ising spin chains in SrHo 2O 4

DOE PAGES

Wen, J. -J.; Tian, W.; Garlea, V. O.; ...

2015-02-26

In this study, we describe why Ising spin chains with competing interactions in SrHo 2O 4 segregate into ordered and disordered ensembles at low temperatures (T). Using elastic neutron scattering, magnetization, and specific heat measurements, the two distinct spin chains are inferred to have Néel (↑↓↑↓) and double-Néel (↑↑↓↓) ground states, respectively. Below T N = 0.68(2)K, the Néel chains develop three-dimensional long range order (LRO), which arrests further thermal equilibration of the double-Néel chains so they remain in a disordered incommensurate state for T below T S = 0.52(2)K. SrHo 2O 4 distills an important feature of incommensurate lowmore » dimensional magnetism: kinetically trapped topological defects in a quasi–d–dimensional spin system can preclude order in d + 1 dimensions.« less

Floating phase in the one-dimensional transverse axial next-nearest-neighbor Ising model.

PubMed

Chandra, Anjan Kumar; Dasgupta, Subinay

2007-02-01

To study the ground state of an axial next-nearest-neighbor Ising chain under transverse field as a function of frustration parameter kappa and field strength Gamma, we present here two different perturbative analyses. In one, we consider the (known) ground state at kappa=0.5 and Gamma=0 as the unperturbed state and treat an increase of the field from 0 to Gamma coupled with an increase of kappa from 0.5 to 0.5+rGamma/J as perturbation. The first-order perturbation correction to eigenvalue can be calculated exactly and we could conclude that there are only two phase-transition lines emanating from the point kappa=0.5, Gamma=0. In the second perturbation scheme, we consider the number of domains of length 1 as the perturbation and obtain the zeroth-order eigenfunction for the perturbed ground state. From the longitudinal spin-spin correlation, we conclude that floating phase exists for small values of transverse field over the entire region intermediate between the ferromagnetic phase and antiphase.

Reentrant behavior in the nearest-neighbor Ising antiferromagnet in a magnetic field

NASA Astrophysics Data System (ADS)

Neto, Minos A.; de Sousa, J. Ricardo

2004-12-01

Motived by the H-T phase diagram in the bcc Ising antiferromagnetic with nearest-neighbor interactions obtained by Monte Carlo simulation [Landau, Phys. Rev. B 16, 4164 (1977)] that shows a reentrant behavior at low temperature, with two critical temperatures in magnetic field about 2% greater than the critical value Hc=8J , we apply the effective field renormalization group (EFRG) approach in this model on three-dimensional lattices (simple cubic-sc and body centered cubic-bcc). We find that the critical curve TN(H) exhibits a maximum point around of H≃Hc only in the bcc lattice case. We also discuss the critical behavior by the effective field theory in clusters with one (EFT-1) and two (EFT-2) spins, and a reentrant behavior is observed for the sc and bcc lattices. We have compared our results of EFRG in the bcc lattice with Monte Carlo and series expansion, and we observe a good accordance between the methods.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

DOE PAGES

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin; ...

2017-11-08

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

On the quantum symmetry of the chiral Ising model

NASA Astrophysics Data System (ADS)

Vecsernyés, Peter

1994-03-01

We introduce the notion of rational Hopf algebras that we think are able to describe the superselection symmetries of rational quantum field theories. As an example we show that a six-dimensional rational Hopf algebra H can reproduce the fusion rules, the conformal weights, the quantum dimensions and the representation of the modular group of the chiral Ising model. H plays the role of the global symmetry algebra of the chiral Ising model in the following sense: (1) a simple field algebra F and a representation π on Hπ of it is given, which contains the c = {1}/{2} unitary representations of the Virasoro algebra as subrepresentations; (2) the embedding U: H → B( Hπ) is such that the observable algebra π( A) - is the invariant subalgebra of B( Hπ) with respect to the left adjoint action of H and U(H) is the commutant of π( A); (3) there exist H-covariant primary fields in B( Hπ), which obey generalized Cuntz algebra properties and intertwine between the inequivalent sectors of the observables.

Compressed quantum computation using a remote five-qubit quantum computer

NASA Astrophysics Data System (ADS)

Hebenstreit, M.; Alsina, D.; Latorre, J. I.; Kraus, B.

2017-05-01

The notion of compressed quantum computation is employed to simulate the Ising interaction of a one-dimensional chain consisting of n qubits using the universal IBM cloud quantum computer running on log2(n ) qubits. The external field parameter that controls the quantum phase transition of this model translates into particular settings of the quantum gates that generate the circuit. We measure the magnetization, which displays the quantum phase transition, on a two-qubit system, which simulates a four-qubit Ising chain, and show its agreement with the theoretical prediction within a certain error. We also discuss the relevant point of how to assess errors when using a cloud quantum computer with a limited amount of runs. As a solution, we propose to use validating circuits, that is, to run independent controlled quantum circuits of similar complexity to the circuit of interest.

Simple universal models capture all classical spin physics.

PubMed

De las Cuevas, Gemma; Cubitt, Toby S

2016-03-11

Spin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. Here, we prove that all the physics of every classical spin model is reproduced in the low-energy sector of certain "universal models," with at most polynomial overhead. This holds for classical models with discrete or continuous degrees of freedom. We prove necessary and sufficient conditions for a spin model to be universal and show that one of the simplest and most widely studied spin models, the two-dimensional Ising model with fields, is universal. Our results may facilitate physical simulations of Hamiltonians with complex interactions. Copyright © 2016, American Association for the Advancement of Science.

From the S U (2 ) quantum link model on the honeycomb lattice to the quantum dimer model on the kagome lattice: Phase transition and fractionalized flux strings

NASA Astrophysics Data System (ADS)

Banerjee, D.; Jiang, F.-J.; Olesen, T. Z.; Orland, P.; Wiese, U.-J.

2018-05-01

We consider the (2 +1 ) -dimensional S U (2 ) quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the kagome lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges [which transform nontrivially under the Z (2 ) center of the S U (2 ) gauge group] are confined to each other by fractionalized strings with a delocalized Z (2 ) flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the three-dimensional Ising universality class separates two confining phases: one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.

Anomalous metastability in a temperature-driven transition

NASA Astrophysics Data System (ADS)

Ibáñez Berganza, M.; Coletti, P.; Petri, A.

2014-06-01

The Langer theory of metastability provides a description of the lifetime and properties of the metastable phase of the Ising model field-driven transition, describing the magnetic-field-driven transition in ferromagnets and the chemical-potential-driven transition of fluids. An immediate further step is to apply it to the study of a transition driven by the temperature, as the one exhibited by the two-dimensional Potts model. For this model, a study based on the analytical continuation of the free energy (Meunier J. L. and Morel A., Eur. Phys. J. B, 13 (2000) 341) predicts the anomalous vanishing of the metastable temperature range in the large-system-size limit, an issue that has been controversial since the eighties. By a GPU algorithm we compare the Monte Carlo dynamics with the theory. For temperatures close to the transition we obtain agreement and characterize the dependence on the system size, which is essentially different with respect to the Ising case. For smaller temperatures, we observe the onset of stationary states with non-Boltzmann statistics, not predicted by the theory.

Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice

NASA Astrophysics Data System (ADS)

Saadatmand, S. N.; Bartlett, S. D.; McCulloch, I. P.

2018-04-01

Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground states of these systems on two-dimensional lattices can be efficiently obtained using state-of-the-art translation-invariant variants of matrix product states and density-matrix renormalization-group algorithms. We use these methods to calculate the fully-quantitative ground-state phase diagram of the long-range interacting triangular Ising model with a transverse field on six-leg infinite-length cylinders and scrutinize the properties of the detected phases. We compare these results with those of the corresponding nearest neighbor model. Our results suggest that, for such long-range Hamiltonians, the long-range quantum fluctuations always lead to long-range correlations, where correlators exhibit power-law decays instead of the conventional exponential drops observed for short-range correlated gapped phases. Our results are relevant for comparisons with recent ion-trap quantum simulator experiments that demonstrate highly-controllable long-range spin couplings for several hundred ions.

Emergent reduced dimensionality by vertex frustration in artificial spin ice

NASA Astrophysics Data System (ADS)

Gilbert, Ian; Lao, Yuyang; Carrasquillo, Isaac; O'Brien, Liam; Watts, Justin D.; Manno, Michael; Leighton, Chris; Scholl, Andreas; Nisoli, Cristiano; Schiffer, Peter

2016-02-01

Reducing the dimensionality of a physical system can have a profound effect on its properties, as in the ordering of low-dimensional magnetic materials, phonon dispersion in mercury chain salts, sliding phases, and the electronic states of graphene. Here we explore the emergence of quasi-one-dimensional behaviour in two-dimensional artificial spin ice, a class of lithographically fabricated nanomagnet arrays used to study geometrical frustration. We extend the implementation of artificial spin ice by fabricating a new array geometry, the so-called tetris lattice. We demonstrate that the ground state of the tetris lattice consists of alternating ordered and disordered bands of nanomagnetic moments. The disordered bands can be mapped onto an emergent thermal one-dimensional Ising model. Furthermore, we show that the level of degeneracy associated with these bands dictates the susceptibility of island moments to thermally induced reversals, thus establishing that vertex frustration can reduce the relevant dimensionality of physical behaviour in a magnetic system.

Emergent reduced dimensionality by vertex frustration in artificial spin ice

DOE PAGES

Gilbert, Ian; Lao, Yuyang; Carrasquillo, Isaac; ...

2015-10-26

Reducing the dimensionality of a physical system can have a profound effect on its properties, as in the ordering of low-dimensional magnetic materials, phonon dispersion in mercury chain salts, sliding phases, and the electronic states of graphene. Here we explore the emergence of quasi-one-dimensional behaviour in two-dimensional artificial spin ice, a class of lithographically fabricated nanomagnet arrays used to study geometrical frustration. We extend the implementation of artificial spin ice by fabricating a new array geometry, the so-called tetris lattice. We demonstrate that the ground state of the tetris lattice consists of alternating ordered and disordered bands of nanomagnetic moments.more » The disordered bands can be mapped onto an emergent thermal one-dimensional Ising model. Furthermore, we show that the level of degeneracy associated with these bands dictates the susceptibility of island moments to thermally induced reversals, thus establishing that vertex frustration can reduce the relevant dimensionality of physical behaviour in a magnetic system.« less

Perpendicular susceptibility and geometrical frustration in two-dimensional Ising antiferromagnets: Exact solutions

NASA Astrophysics Data System (ADS)

Muttalib, K. A.; Khatun, M.; Barry, J. H.

2017-11-01

Discovery of new materials and improved experimental as well as numerical techniques have led to a renewed interest in geometrically frustrated spin systems. However, there are very few exact results available that can provide a benchmark for comparison. In this work, we calculate exactly the perpendicular susceptibility χ⊥ for an Ising antiferromagnet with (i) nearest-neighbor pair interaction on a kagome lattice where strong frustration prevents long-range ordering and (ii) elementary triplet interactions on a kagome lattice which has no frustration but the system remains disordered down to zero temperature. By comparing with other known exact results with and without frustration, we propose that an appropriately temperature-scaled χ⊥ can be used as a quantitative measure of the degree of frustration in Ising spin systems.

Quantum quenches in two spatial dimensions using chain array matrix product states

DOE PAGES

A. J. A. James; Konik, R.

2015-10-15

We describe a method for simulating the real time evolution of extended quantum systems in two dimensions (2D). The method combines the benefits of integrability and matrix product states in one dimension to avoid several issues that hinder other applications of tensor based methods in 2D. In particular, it can be extended to infinitely long cylinders. As an example application we present results for quantum quenches in the 2D quantum [(2+1)-dimensional] Ising model. As a result, in quenches that cross a phase boundary we find that the return probability shows nonanalyticities in time.

Multipoint Green's functions in 1 + 1 dimensional integrable quantum field theories

DOE PAGES

Babujian, H. M.; Karowski, M.; Tsvelik, A. M.

2017-02-14

We calculate the multipoint Green functions in 1+1 dimensional integrable quantum field theories. We use the crossing formula for general models and calculate the 3 and 4 point functions taking in to account only the lower nontrivial intermediate states contributions. Then we apply the general results to the examples of the scaling Z 2 Ising model, sinh-Gordon model and Z 3 scaling Potts model. We demonstrate this calculations explicitly. The results can be applied to physical phenomena as for example to the Raman scattering.

Nonequilibrium critical behavior of model statistical systems and methods for the description of its features

NASA Astrophysics Data System (ADS)

Prudnikov, V. V.; Prudnikov, P. V.; Mamonova, M. V.

2017-11-01

This paper reviews features in critical behavior of far-from-equilibrium macroscopic systems and presents current methods of describing them by referring to some model statistical systems such as the three-dimensional Ising model and the two-dimensional XY model. The paper examines the critical relaxation of homogeneous and structurally disordered systems subjected to abnormally strong fluctuation effects involved in ordering processes in solids at second-order phase transitions. Interest in such systems is due to the aging properties and fluctuation-dissipation theorem violations predicted for and observed in systems slowly evolving from a nonequilibrium initial state. It is shown that these features of nonequilibrium behavior show up in the magnetic properties of magnetic superstructures consisting of alternating nanoscale-thick magnetic and nonmagnetic layers and can be observed not only near the film’s critical ferromagnetic ordering temperature Tc, but also over the wide temperature range T ⩽ Tc.

Defect-phase-dynamics approach to statistical domain-growth problem of clock models

NASA Technical Reports Server (NTRS)

Kawasaki, K.

1985-01-01

The growth of statistical domains in quenched Ising-like p-state clock models with p = 3 or more is investigated theoretically, reformulating the analysis of Ohta et al. (1982) in terms of a phase variable and studying the dynamics of defects introduced into the phase field when the phase variable becomes multivalued. The resulting defect/phase domain-growth equation is applied to the interpretation of Monte Carlo simulations in two dimensions (Kaski and Gunton, 1983; Grest and Srolovitz, 1984), and problems encountered in the analysis of related Potts models are discussed. In the two-dimensional case, the problem is essentially that of a purely dissipative Coulomb gas, with a sq rt t growth law complicated by vertex-pinning effects at small t.

Numerical tests of local scale invariance in ageing q-state Potts models

NASA Astrophysics Data System (ADS)

Lorenz, E.; Janke, W.

2007-01-01

Much effort has been spent over the last years to achieve a coherent theoretical description of ageing as a non-linear dynamics process. Long supposed to be a consequence of the slow dynamics of glassy systems only, ageing phenomena could also be identified in the phase-ordering kinetics of simple ferromagnets. As a phenomenological approach Henkel et al. developed a group of local scale transformations under which two-time autocorrelation and response functions should transform covariantly. This work is to extend previous numerical tests of the predicted scaling functions for the Ising model by Monte Carlo simulations of two-dimensional q-state Potts models with q=3 and 8, which, in equilibrium, undergo temperature-driven phase transitions of second and first order, respectively.

Effect of External Economic-Field Cycle and Market Temperature on Stock-Price Hysteresis: Monte Carlo Simulation on the Ising Spin Model

NASA Astrophysics Data System (ADS)

Punya Jaroenjittichai, Atchara; Laosiritaworn, Yongyut

2017-09-01

In this work, the stock-price versus economic-field hysteresis was investigated. The Ising spin Hamiltonian was utilized as the level of ‘disagreement’ in describing investors’ behaviour. The Ising spin directions were referred to an investor’s intention to perform his action on trading his stock. The periodic economic variation was also considered via the external economic-field in the Ising model. The stochastic Monte Carlo simulation was performed on Ising spins, where the steady-state excess demand and supply as well as the stock-price were extracted via the magnetization. From the results, the economic-field parameters and market temperature were found to have significant effect on the dynamic magnetization and stock-price behaviour. Specifically, the hysteresis changes from asymmetric to symmetric loops with increasing market temperature and economic-field strength. However, the hysteresis changes from symmetric to asymmetric loops with increasing the economic-field frequency, when either temperature or economic-field strength is large enough, and returns to symmetric shape at very high frequencies. This suggests competitive effects among field and temperature factors on the hysteresis characteristic, implying multi-dimensional complicated non-trivial relationship among inputs-outputs. As is seen, the results reported (over extensive range) can be used as basis/guideline for further analysis/quantifying how economic-field and market-temperature affect the stock-price distribution on the course of economic cycle.

Accurate estimates of 3D Ising critical exponents using the coherent-anomaly method

NASA Astrophysics Data System (ADS)

Kolesik, Miroslav; Suzuki, Masuo

1995-02-01

An analysis of the critical behavior of the three-dimensional Ising model using the coherent-anomaly method (CAM) is presented. Various sources of errors in CAM estimates of critical exponents are discussed, and an improved scheme for the CAM data analysis is tested. Using a set of mean-field type approximations based on the variational series expansion approach, accuracy comparable to the most precise conventional methods has been achieved. Our results for the critical exponents are given by α = 0.108(5), β = 0.327(4), γ = 1.237(4) and δ = 4.77(5).

Cosmic ray composition investigations using ICE/ISEE-3

NASA Technical Reports Server (NTRS)

Wiedenbeck, Mark E.

1992-01-01

The analysis of data from the high energy cosmic experiment on ISEE-3 and associated modeling and interpretation activities are discussed. The ISEE-3 payload included two instruments capable of measuring the composition of heavy cosmic rays. The designs of these two instruments incorporated innovations which made it possible, for the first time, to measure isotopic as well as the chemical composition for a wide range of elements. As the result of the demonstrations by these two instruments of the capability to resolve individual cosmic ray isotopes, a new generation of detectors was developed using very similar designs, but having improved reliability and increased sensitive area. The composition measurements which were obtained from the ISEE-3 experiment are summarized.

Towards Simulating the Transverse Ising Model in a 2D Array of Trapped Ions

NASA Astrophysics Data System (ADS)

Sawyer, Brian

2013-05-01

Two-dimensional Coulomb crystals provide a useful platform for large-scale quantum simulation. Penning traps enable confinement of large numbers of ions (>100) and allow for the tunable-range spin-spin interactions demonstrated in linear ion strings, facilitating simulation of quantum magnetism at a scale that is currently intractable on classical computers. We readily confine hundreds of Doppler laser-cooled 9Be+ within a Penning trap, producing a planar array of ions with self-assembled triangular order. The transverse ``drumhead'' modes of our 2D crystal along with the valence electron spin of Be+ serve as a resource for generating spin-motion and spin-spin entanglement. Applying a spin-dependent optical dipole force (ODF) to the ion array, we perform spectroscopy and thermometry of individual drumhead modes. This ODF also allows us to engineer long-range Ising spin couplings of either ferromagnetic or anti-ferromagnetic character whose approximate power-law scaling with inter-ion distance, d, may be varied continuously from 1 /d0 to 1 /d3. An effective transverse magnetic field is applied via microwave radiation at the ~124-GHz spin-flip frequency, and ground states of the effective Ising Hamiltonian may in principle be prepared adiabatically by slowly decreasing this transverse field in the presence of the induced Ising coupling. Long-range anti-ferromagnetic interactions are of particular interest due to their inherent spin frustration and resulting large, near-degenerate manifold of ground states. We acknowledge support from NIST and the DARPA-OLE program.

Selective Transient Cooling by Impulse Perturbations in a Simple Toy Model

NASA Astrophysics Data System (ADS)

Fabrizio, Michele

2018-06-01

We show in a simple exactly solvable toy model that a properly designed impulse perturbation can transiently cool down low-energy degrees of freedom at the expense of high-energy ones that heat up. The model consists of two infinite-range quantum Ising models: one, the high-energy sector, with a transverse field much bigger than the other, the low-energy sector. The finite-duration perturbation is a spin exchange that couples the two Ising models with an oscillating coupling strength. We find a cooling of the low-energy sector that is optimized by the oscillation frequency in resonance with the spin exchange excitation. After the perturbation is turned off, the Ising model with a low transverse field can even develop a spontaneous symmetry breaking despite being initially above the critical temperature.

Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping

NASA Astrophysics Data System (ADS)

Kubica, Aleksander; Beverland, Michael E.; Brandão, Fernando; Preskill, John; Svore, Krysta M.

2018-05-01

Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code (3DCC) on the body-centered cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D stringlike and 2D sheetlike logical operators to be p3DCC (1 )≃1.9 % and p3DCC (2 )≃27.6 % . We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the four- and six-body random coupling Ising models.

Orthogonal Polynomials on the Unit Circle with Fibonacci Verblunsky Coefficients, II. Applications

NASA Astrophysics Data System (ADS)

Damanik, David; Munger, Paul; Yessen, William N.

2013-10-01

We consider CMV matrices with Verblunsky coefficients determined in an appropriate way by the Fibonacci sequence and present two applications of the spectral theory of such matrices to problems in mathematical physics. In our first application we estimate the spreading rates of quantum walks on the line with time-independent coins following the Fibonacci sequence. The estimates we obtain are explicit in terms of the parameters of the system. In our second application, we establish a connection between the classical nearest neighbor Ising model on the one-dimensional lattice in the complex magnetic field regime, and CMV operators. In particular, given a sequence of nearest-neighbor interaction couplings, we construct a sequence of Verblunsky coefficients, such that the support of the Lee-Yang zeros of the partition function for the Ising model in the thermodynamic limit coincides with the essential spectrum of the CMV matrix with the constructed Verblunsky coefficients. Under certain technical conditions, we also show that the zeros distribution measure coincides with the density of states measure for the CMV matrix.

Statistical mechanics of the cluster Ising model

NASA Astrophysics Data System (ADS)

Smacchia, Pietro; Amico, Luigi; Facchi, Paolo; Fazio, Rosario; Florio, Giuseppe; Pascazio, Saverio; Vedral, Vlatko

2011-08-01

We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.

Quantum mean-field approximation for lattice quantum models: Truncating quantum correlations and retaining classical ones

NASA Astrophysics Data System (ADS)

Malpetti, Daniele; Roscilde, Tommaso

2017-02-01

The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical approaches based on an approximate, yet systematically improved account of quantum correlations.

Transverse spin correlations of the random transverse-field Ising model

NASA Astrophysics Data System (ADS)

Iglói, Ferenc; Kovács, István A.

2018-03-01

The critical behavior of the random transverse-field Ising model in finite-dimensional lattices is governed by infinite disorder fixed points, several properties of which have already been calculated by the use of the strong disorder renormalization-group (SDRG) method. Here we extend these studies and calculate the connected transverse-spin correlation function by a numerical implementation of the SDRG method in d =1 ,2 , and 3 dimensions. At the critical point an algebraic decay of the form ˜r-ηt is found, with a decay exponent being approximately ηt≈2 +2 d . In d =1 the results are related to dimer-dimer correlations in the random antiferromagnetic X X chain and have been tested by numerical calculations using free-fermionic techniques.

Volatility behavior of visibility graph EMD financial time series from Ising interacting system

NASA Astrophysics Data System (ADS)

Zhang, Bo; Wang, Jun; Fang, Wen

2015-08-01

A financial market dynamics model is developed and investigated by stochastic Ising system, where the Ising model is the most popular ferromagnetic model in statistical physics systems. Applying two graph based analysis and multiscale entropy method, we investigate and compare the statistical volatility behavior of return time series and the corresponding IMF series derived from the empirical mode decomposition (EMD) method. And the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model. Further, we find that the degree distribution of visibility graph for the simulation series has the power law tails, and the assortative network exhibits the mixing pattern property. All these features are in agreement with the real market data, the research confirms that the financial model established by the Ising system is reasonable.

Critical excitation spectrum of a quantum chain with a local three-spin coupling.

PubMed

McCabe, John F; Wydro, Tomasz

2011-09-01

Using the phenomenological renormalization group (PRG), we evaluate the low-energy excitation spectrum along the critical line of a quantum spin chain having a local interaction between three Ising spins and longitudinal and transverse magnetic fields, i.e., a Turban model. The low-energy excitation spectrum found with the PRG agrees with the spectrum predicted for the (D(4),A(4)) conformal minimal model under a nontrivial correspondence between translations at the critical line and discrete lattice translations. Under this correspondence, the measurements confirm a prediction that the critical line of this quantum spin chain and the critical point of the two-dimensional three-state Potts model are in the same universality class.

Quantum cluster variational method and message passing algorithms revisited

NASA Astrophysics Data System (ADS)

Domínguez, E.; Mulet, Roberto

2018-02-01

We present a general framework to study quantum disordered systems in the context of the Kikuchi's cluster variational method (CVM). The method relies in the solution of message passing-like equations for single instances or in the iterative solution of complex population dynamic algorithms for an average case scenario. We first show how a standard application of the Kikuchi's CVM can be easily translated to message passing equations for specific instances of the disordered system. We then present an "ad hoc" extension of these equations to a population dynamic algorithm representing an average case scenario. At the Bethe level, these equations are equivalent to the dynamic population equations that can be derived from a proper cavity ansatz. However, at the plaquette approximation, the interpretation is more subtle and we discuss it taking also into account previous results in classical disordered models. Moreover, we develop a formalism to properly deal with the average case scenario using a replica-symmetric ansatz within this CVM for quantum disordered systems. Finally, we present and discuss numerical solutions of the different approximations for the quantum transverse Ising model and the quantum random field Ising model in two-dimensional lattices.

Thermodynamics of Ising spins on the triangular kagome lattice: Exact analytical method and Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Loh, Y. L.; Yao, D. X.; Carlson, E. W.

2008-04-01

A new class of two-dimensional magnetic materials Cu9X2(cpa)6ṡxH2O ( cpa=2 -carboxypentonic acid; X=F,Cl,Br ) was recently fabricated in which Cu sites form a triangular kagome lattice (TKL). As the simplest model of geometric frustration in such a system, we study the thermodynamics of Ising spins on the TKL using exact analytic method as well as Monte Carlo simulations. We present the free energy, internal energy, specific heat, entropy, sublattice magnetizations, and susceptibility. We describe the rich phase diagram of the model as a function of coupling constants, temperature, and applied magnetic field. For frustrated interactions in the absence of applied field, the ground state is a spin liquid phase with residual entropy per spin s0/kB=(1)/(9)ln72≈0.4752… . In weak applied field, the system maps to the dimer model on a honeycomb lattice, with residual entropy 0.0359 per spin and quasi-long-range order with power-law spin-spin correlations that should be detectable by neutron scattering. The power-law correlations become exponential at finite temperatures, but the correlation length may still be long.

Engineered spin-spin interactions on a 2D array of trapped ions

NASA Astrophysics Data System (ADS)

Britton, Joe; Sawyer, Brian; Bollinger, John

2013-05-01

We work with laser cooled 9Be+ ions confined in a Penning trap to simulate quantum magnetic interactions. The valence electron of each ion behaves as an ideal spin- 1 / 2 particle. We recently demonstrated a uniform anti-ferromagnetic Ising interaction on a naturally occurring two-dimensional (2D) triangular crystal of 100 < N < 350 ions. The Ising interaction is generated by a spin-dependent optical dipole force (ODF). For spins separated by distance d, we show that the range can be tuned according to (d / d 0)-a, for 0 < a < 3 . For different operating parameters we can also generate an infinite range ferromagnetic Ising interaction. We also use the ODF for spectroscopy and thermometry of the normal modes of the trapped ion array. A detailed understanding of the modes is important because they mediate the spin-spin interactions. This work is supported by NIST and the DARPA OLE program.

Ising antiferromagnet on the Archimedean lattices.

PubMed

Yu, Unjong

2015-06-01

Geometric frustration effects were studied systematically with the Ising antiferromagnet on the 11 Archimedean lattices using the Monte Carlo methods. The Wang-Landau algorithm for static properties (specific heat and residual entropy) and the Metropolis algorithm for a freezing order parameter were adopted. The exact residual entropy was also found. Based on the degree of frustration and dynamic properties, ground states of them were determined. The Shastry-Sutherland lattice and the trellis lattice are weakly frustrated and have two- and one-dimensional long-range-ordered ground states, respectively. The bounce, maple-leaf, and star lattices have the spin ice phase. The spin liquid phase appears in the triangular and kagome lattices.

Ising antiferromagnet on the Archimedean lattices

NASA Astrophysics Data System (ADS)

Yu, Unjong

2015-06-01

Geometric frustration effects were studied systematically with the Ising antiferromagnet on the 11 Archimedean lattices using the Monte Carlo methods. The Wang-Landau algorithm for static properties (specific heat and residual entropy) and the Metropolis algorithm for a freezing order parameter were adopted. The exact residual entropy was also found. Based on the degree of frustration and dynamic properties, ground states of them were determined. The Shastry-Sutherland lattice and the trellis lattice are weakly frustrated and have two- and one-dimensional long-range-ordered ground states, respectively. The bounce, maple-leaf, and star lattices have the spin ice phase. The spin liquid phase appears in the triangular and kagome lattices.

Dynamical implications of sample shape for avalanches in 2-dimensional random-field Ising model with saw-tooth domain wall

NASA Astrophysics Data System (ADS)

Tadić, Bosiljka

2018-03-01

We study dynamics of a built-in domain wall (DW) in 2-dimensional disordered ferromagnets with different sample shapes using random-field Ising model on a square lattice rotated by 45 degrees. The saw-tooth DW of the length Lx is created along one side and swept through the sample by slow ramping of the external field until the complete magnetisation reversal and the wall annihilation at the open top boundary at a distance Ly. By fixing the number of spins N =Lx ×Ly = 106 and the random-field distribution at a value above the critical disorder, we vary the ratio of the DW length to the annihilation distance in the range Lx /Ly ∈ [ 1 / 16 , 16 ] . The periodic boundary conditions are applied in the y-direction so that these ratios comprise different samples, i.e., surfaces of cylinders with the changing perimeter Lx and height Ly. We analyse the avalanches of the DW slips between following field updates, and the multifractal structure of the magnetisation fluctuation time series. Our main findings are that the domain-wall lengths materialised in different sample shapes have an impact on the dynamics at all scales. Moreover, the domain-wall motion at the beginning of the hysteresis loop (HLB) probes the disorder effects resulting in the fluctuations that are significantly different from the large avalanches in the central part of the loop (HLC), where the strong fields dominate. Specifically, the fluctuations in HLB exhibit a wide multi-fractal spectrum, which shifts towards higher values of the exponents when the DW length is reduced. The distributions of the avalanches in this segments of the loops obey power-law decay and the exponential cutoffs with the exponents firmly in the mean-field universality class for long DW. In contrast, the avalanches in the HLC obey Tsallis density distribution with the power-law tails which indicate the new categories of the scale invariant behaviour for different ratios Lx /Ly. The large fluctuations in the HLC, on the other hand, have a rather narrow spectrum which is less sensitive to the length of the wall. These findings shed light to the dynamical criticality of the random-field Ising model at its lower critical dimension; they can be relevant to applications of the dynamics of injected domain walls in two-dimensional nanowires and ferromagnetic films.

Deep Neural Network Detects Quantum Phase Transition

NASA Astrophysics Data System (ADS)

Arai, Shunta; Ohzeki, Masayuki; Tanaka, Kazuyuki

2018-03-01

We detect the quantum phase transition of a quantum many-body system by mapping the observed results of the quantum state onto a neural network. In the present study, we utilized the simplest case of a quantum many-body system, namely a one-dimensional chain of Ising spins with the transverse Ising model. We prepared several spin configurations, which were obtained using repeated observations of the model for a particular strength of the transverse field, as input data for the neural network. Although the proposed method can be employed using experimental observations of quantum many-body systems, we tested our technique with spin configurations generated by a quantum Monte Carlo simulation without initial relaxation. The neural network successfully identified the strength of transverse field only from the spin configurations, leading to consistent estimations of the critical point of our model Γc = J.

Realization of the axial next-nearest-neighbor Ising model in U 3 Al 2 Ge 3

DOE PAGES

Fobes, David M.; Lin, Shi-Zeng; Ghimire, Nirmal J.; ...

2017-11-09

Inmore » this paper, we report small-angle neutron scattering (SANS) measurements and theoretical modeling of U 3 Al 2 Ge 3 . Analysis of the SANS data reveals a phase transition to sinusoidally modulated magnetic order at T N = 63 K to be second order and a first-order phase transition to ferromagnetic order at T c = 48 K. Within the sinusoidally modulated magnetic phase (T c < T < T N), we uncover a dramatic change, by a factor of 3, in the ordering wave vector as a function of temperature. Finally, these observations all indicate that U 3 Al 2 Ge 3 is a close realization of the three-dimensional axial next-nearest-neighbor Ising model, a prototypical framework for describing commensurate to incommensurate phase transitions in frustrated magnets.« less

Realization of the axial next-nearest-neighbor Ising model in U 3 Al 2 Ge 3

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fobes, David M.; Lin, Shi-Zeng; Ghimire, Nirmal J.

Inmore » this paper, we report small-angle neutron scattering (SANS) measurements and theoretical modeling of U 3 Al 2 Ge 3 . Analysis of the SANS data reveals a phase transition to sinusoidally modulated magnetic order at T N = 63 K to be second order and a first-order phase transition to ferromagnetic order at T c = 48 K. Within the sinusoidally modulated magnetic phase (T c < T < T N), we uncover a dramatic change, by a factor of 3, in the ordering wave vector as a function of temperature. Finally, these observations all indicate that U 3 Al 2 Ge 3 is a close realization of the three-dimensional axial next-nearest-neighbor Ising model, a prototypical framework for describing commensurate to incommensurate phase transitions in frustrated magnets.« less

Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping.

PubMed

Kubica, Aleksander; Beverland, Michael E; Brandão, Fernando; Preskill, John; Svore, Krysta M

2018-05-04

Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code (3DCC) on the body-centered cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D stringlike and 2D sheetlike logical operators to be p_{3DCC}^{(1)}≃1.9% and p_{3DCC}^{(2)}≃27.6%. We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the four- and six-body random coupling Ising models.

Learning planar Ising models

DOE PAGES

Johnson, Jason K.; Oyen, Diane Adele; Chertkov, Michael; ...

2016-12-01

Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a greedy algorithm for learning the bestmore » planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. Finally, we demonstrate our method in simulations and for two applications: modeling senate voting records and identifying geo-chemical depth trends from Mars rover data.« less

Learning planar Ising models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Jason K.; Oyen, Diane Adele; Chertkov, Michael

Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a greedy algorithm for learning the bestmore » planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. Finally, we demonstrate our method in simulations and for two applications: modeling senate voting records and identifying geo-chemical depth trends from Mars rover data.« less

Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination

NASA Astrophysics Data System (ADS)

Hu, Wenjian; Singh, Rajiv R. P.; Scalettar, Richard T.

2017-06-01

We apply unsupervised machine learning techniques, mainly principal component analysis (PCA), to compare and contrast the phase behavior and phase transitions in several classical spin models—the square- and triangular-lattice Ising models, the Blume-Capel model, a highly degenerate biquadratic-exchange spin-1 Ising (BSI) model, and the two-dimensional X Y model—and we examine critically what machine learning is teaching us. We find that quantified principal components from PCA not only allow the exploration of different phases and symmetry-breaking, but they can distinguish phase-transition types and locate critical points. We show that the corresponding weight vectors have a clear physical interpretation, which is particularly interesting in the frustrated models such as the triangular antiferromagnet, where they can point to incipient orders. Unlike the other well-studied models, the properties of the BSI model are less well known. Using both PCA and conventional Monte Carlo analysis, we demonstrate that the BSI model shows an absence of phase transition and macroscopic ground-state degeneracy. The failure to capture the "charge" correlations (vorticity) in the BSI model (X Y model) from raw spin configurations points to some of the limitations of PCA. Finally, we employ a nonlinear unsupervised machine learning procedure, the "autoencoder method," and we demonstrate that it too can be trained to capture phase transitions and critical points.

Anisotropy of stress correlation in two-dimensional liquids and a pseudospin model

DOE PAGES

Wu, Bin; Iwashita, Takuya; Egami, Takeshi

2015-11-04

Liquids are condensed matter in which atoms are strongly correlated in position and momentum. The atomic pair density function (PDF) is used often in describing such correlation. However, elucidation of many properties requires higher degrees of correlation than the pair correlation. For instance, viscosity depends upon the stress correlations in space and time. We examine the cross correlation between the stress correlation at the atomic level and the PDF for two-dimensional liquids. We introduce the concept of the stress-resolved pair distribution function (SRPDF) that uses the sign of atomic-level stress as a selection rule to include particles from density correlations.more » The connection between SRPDFs and stress correlation function is explained through an approximation in which the shear stress is replaced by a pseudospin. Lastly, we further assess the possibility of interpreting the long-range stress correlation as a consequence of short-range Ising-like pseudospin interactions.« less

Information transport in classical statistical systems

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-02-01

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.

Quantum chaos in the Heisenberg spin chain: The effect of Dzyaloshinskii-Moriya interaction.

PubMed

Vahedi, J; Ashouri, A; Mahdavifar, S

2016-10-01

Using one-dimensional spin-1/2 systems as prototypes of quantum many-body systems, we study the emergence of quantum chaos. The main purpose of this work is to answer the following question: how the spin-orbit interaction, as a pure quantum interaction, may lead to the onset of quantum chaos? We consider the three integrable spin-1/2 systems: the Ising, the XX, and the XXZ limits and analyze whether quantum chaos develops or not after the addition of the Dzyaloshinskii-Moriya interaction. We find that depending on the strength of the anisotropy parameter, the answer is positive for the XXZ and Ising models, whereas no such evidence is observed for the XX model. We also discuss the relationship between quantum chaos and thermalization.

Model parameter learning using Kullback-Leibler divergence

NASA Astrophysics Data System (ADS)

Lin, Chungwei; Marks, Tim K.; Pajovic, Milutin; Watanabe, Shinji; Tung, Chih-kuan

2018-02-01

In this paper, we address the following problem: For a given set of spin configurations whose probability distribution is of the Boltzmann type, how do we determine the model coupling parameters? We demonstrate that directly minimizing the Kullback-Leibler divergence is an efficient method. We test this method against the Ising and XY models on the one-dimensional (1D) and two-dimensional (2D) lattices, and provide two estimators to quantify the model quality. We apply this method to two types of problems. First, we apply it to the real-space renormalization group (RG). We find that the obtained RG flow is sufficiently good for determining the phase boundary (within 1% of the exact result) and the critical point, but not accurate enough for critical exponents. The proposed method provides a simple way to numerically estimate amplitudes of the interactions typically truncated in the real-space RG procedure. Second, we apply this method to the dynamical system composed of self-propelled particles, where we extract the parameter of a statistical model (a generalized XY model) from a dynamical system described by the Viscek model. We are able to obtain reasonable coupling values corresponding to different noise strengths of the Viscek model. Our method is thus able to provide quantitative analysis of dynamical systems composed of self-propelled particles.

Multipartite entanglement characterization of a quantum phase transition

NASA Astrophysics Data System (ADS)

Costantini, G.; Facchi, P.; Florio, G.; Pascazio, S.

2007-07-01

A probability density characterization of multipartite entanglement is tested on the one-dimensional quantum Ising model in a transverse field. The average and second moment of the probability distribution are numerically shown to be good indicators of the quantum phase transition. We comment on multipartite entanglement generation at a quantum phase transition.

Critical behavior of two- and three-dimensional ferromagnetic and antiferromagnetic spin-ice systems using the effective-field renormalization group technique

NASA Astrophysics Data System (ADS)

Garcia-Adeva, Angel J.; Huber, David L.

2001-07-01

In this work we generalize and subsequently apply the effective-field renormalization-group (EFRG) technique to the problem of ferro- and antiferromagnetically coupled Ising spins with local anisotropy axes in geometrically frustrated geometries (kagomé and pyrochlore lattices). In this framework, we calculate the various ground states of these systems and the corresponding critical points. Excellent agreement is found with exact and Monte Carlo results. The effects of frustration are discussed. As pointed out by other authors, it turns out that the spin-ice model can be exactly mapped to the standard Ising model, but with effective interactions of the opposite sign to those in the original Hamiltonian. Therefore, the ferromagnetic spin ice is frustrated and does not order. Antiferromagnetic spin ice (in both two and three dimensions) is found to undergo a transition to a long-range-ordered state. The thermal and magnetic critical exponents for this transition are calculated. It is found that the thermal exponent is that of the Ising universality class, whereas the magnetic critical exponent is different, as expected from the fact that the Zeeman term has a different symmetry in these systems. In addition, the recently introduced generalized constant coupling method is also applied to the calculation of the critical points and ground-state configurations. Again, a very good agreement is found with exact, Monte Carlo, and renormalization-group calculations for the critical points. Incidentally, we show that the generalized constant coupling approach can be regarded as the lowest-order limit of the EFRG technique, in which correlations outside a frustrated unit are neglected, and scaling is substituted by strict equality of the thermodynamic quantities.

Nonequilibrium umbrella sampling in spaces of many order parameters

NASA Astrophysics Data System (ADS)

Dickson, Alex; Warmflash, Aryeh; Dinner, Aaron R.

2009-02-01

We recently introduced an umbrella sampling method for obtaining nonequilibrium steady-state probability distributions projected onto an arbitrary number of coordinates that characterize a system (order parameters) [A. Warmflash, P. Bhimalapuram, and A. R. Dinner, J. Chem. Phys. 127, 154112 (2007)]. Here, we show how our algorithm can be combined with the image update procedure from the finite-temperature string method for reversible processes [E. Vanden-Eijnden and M. Venturoli, "Revisiting the finite temperature string method for calculation of reaction tubes and free energies," J. Chem. Phys. (in press)] to enable restricted sampling of a nonequilibrium steady state in the vicinity of a path in a many-dimensional space of order parameters. For the study of transitions between stable states, the adapted algorithm results in improved scaling with the number of order parameters and the ability to progressively refine the regions of enforced sampling. We demonstrate the algorithm by applying it to a two-dimensional model of driven Brownian motion and a coarse-grained (Ising) model for nucleation under shear. It is found that the choice of order parameters can significantly affect the convergence of the simulation; local magnetization variables other than those used previously for sampling transition paths in Ising systems are needed to ensure that the reactive flux is primarily contained within a tube in the space of order parameters. The relation of this method to other algorithms that sample the statistics of path ensembles is discussed.

Quasi-one-dimensional magnetism in MnxFe1-xNb2O6 compounds: From Heisenberg to Ising chains

NASA Astrophysics Data System (ADS)

Hneda, M. L.; Oliveira Neto, S. R.; da Cunha, J. B. M.; Gusmão, M. A.; Isnard, O.

2018-06-01

A series of MnxFe1-xNb2O6 compounds (0 ⩽ x ⩽ 1) is investigated by both X-ray and neutron powder diffraction, as well as specific-heat and magnetic measurements. The samples present orthorhombic Pbcn crystal symmetry, and exhibit weakly coupled magnetic chains. These chains are of Heisenberg type (weak anisotropy) on the Mn-rich side, and Ising-like (strong anisotropy) on the Fe-rich side. Except for 100% Fe (x = 0) , which has weakly-interacting ferromagnetic Ising chains, a negative Curie-Weiss temperature is obtained from the magnetic susceptibility, indicating dominant antiferromagnetic interactions. At the lowest probed temperature, T = 1.5K , true long-range magnetic order is only observed for x = 1 , 0.8, and 0. Although the ordering is globally antiferromagnetic in all cases, the first two are characterized by a two-sublattice structure with propagation vector k = (0, 0, 0) , while the latter presents alternatingly oriented ferromagnetic chains described by k = (0,1/2, 0) . For other compositions, short-range magnetic correlations are extracted from diffuse neutron-scattering data.

Gaps between avalanches in one-dimensional random-field Ising models

NASA Astrophysics Data System (ADS)

Nampoothiri, Jishnu N.; Ramola, Kabir; Sabhapandit, Sanjib; Chakraborty, Bulbul

2017-09-01

We analyze the statistics of gaps (Δ H ) between successive avalanches in one-dimensional random-field Ising models (RFIMs) in an external field H at zero temperature. In the first part of the paper we study the nearest-neighbor ferromagnetic RFIM. We map the sequence of avalanches in this system to a nonhomogeneous Poisson process with an H -dependent rate ρ (H ) . We use this to analytically compute the distribution of gaps P (Δ H ) between avalanches as the field is increased monotonically from -∞ to +∞ . We show that P (Δ H ) tends to a constant C (R ) as Δ H →0+ , which displays a nontrivial behavior with the strength of disorder R . We verify our predictions with numerical simulations. In the second part of the paper, motivated by avalanche gap distributions in driven disordered amorphous solids, we study a long-range antiferromagnetic RFIM. This model displays a gapped behavior P (Δ H )=0 up to a system size dependent offset value Δ Hoff , and P (Δ H ) ˜(ΔH -Δ Hoff) θ as Δ H →Hoff+ . We perform numerical simulations on this model and determine θ ≈0.95 (5 ) . We also discuss mechanisms which would lead to a nonzero exponent θ for general spin models with quenched random fields.

An Experimental Study of the Ising Chain Statistics under the Magnetic Field

NASA Astrophysics Data System (ADS)

Takeda, Kazuyoshi; Wada, Masaru

1981-11-01

The first experimental study of the statistics of a quasi-one-dimensional Ising system under the magnetic field Hα, described by the Hamiltonian \\includegraphics{dummy.eps} has been performed, where J1 and J2 are the intra- and the inter-chain exchange constants, respectively. A single crystal of the compound (CH3)3NHCoCl3\\cdot2H2O has been used as a model sample of the ferromagnetic system with J1/kB{=}14.2 K and J2/kB{=}0.20 K. It has been revealed that the experimental values of the magnetic heat capacity under the field Hα>2J2/gzμB (≈0.8 kOe) applied along the spin preferential axis are excellently reproduced by the values calculated for the isolated Ising chain under the longitudinal field (α{=}z; gz{=}6.54). For the temperature higher than 7 K (≈J1/2kB), the experimental values of the magnetic heat capacity under the field along the spin hard axis have also agreed with the theoretical values for the isolated Ising chain under the transverse field (α{=}y; gy{=}3.90).

Depinning transition of a domain wall in ferromagnetic films

DOE PAGES

Xi, Bin; Luo, Meng -Bo; Vinokur, Valerii M.; ...

2015-09-14

Here, we report first principle numerical study of domain wall (DW) depinning in two-dimensional magnetic film, which is modeled by 2D random-field Ising system with the dipole-dipole interaction. We observe non-conventional activation-type motion of DW and reveal the fractal structure of DW near the depinning transition. We determine scaling functions describing critical dynamics near the transition and obtain universal exponents establishing connection between thermal softening of pinning potential and critical dynamics. In addition, we observe that tuning the strength of the dipole-dipole interaction switches DW dynamics between two different universality classes, corresponding to two distinct dynamic regimes characterized by non-Arrheniusmore » and conventional Arrhenius-type DW motions.« less

Quantum phase transition between cluster and antiferromagnetic states

NASA Astrophysics Data System (ADS)

Son, W.; Amico, L.; Fazio, R.; Hamma, A.; Pascazio, S.; Vedral, V.

2011-09-01

We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like exchange. We show that the ground state in the cluster phase possesses symmetry protected topological order. A continuous quantum phase transition occurs as result of the competition between the cluster and Ising terms. At the critical point the Hamiltonian is self-dual. The geometric entanglement is also studied and used to investigate the quantum phase transition. Our findings in one dimension corroborate the analysis of the two-dimensional generalization of the system, indicating, at a mean-field level, the presence of a direct transition between an antiferromagnetic and a valence bond solid ground state.

Engineered long-range interactions on a 2D array of trapped ions

NASA Astrophysics Data System (ADS)

Britton, Joseph W.; Sawyer, Brian C.; Bollinger, John J.; Freericks, James K.

2014-03-01

Ising interactions are one paradigm used to model quantum magnetism in condensed matter systems. At NIST Boulder we confine and Doppler laser cool hundreds of 9Be+ ions in a Penning trap. The valence electron of each ion behaves as an ideal spin-1/2 particle and, in the limit of weak radial confinement relative to axial confinement, the ions naturally form a two-dimensional triangular lattice. A variable-range anti-ferromagnetic Ising interaction is engineered with a spin-dependent optical dipole force (ODF) through spin-dependent excitation of collective modes of ion motion. We have also exploited this spin-dependent force to perform spectroscopy and thermometry of the normal modes of the trapped ion crystal. The high spin-count and long-range spin-spin couplings achievable in the NIST Penning trap brings within reach simulation of computationally intractable problems in quantum magnetism. Examples include modeling quantum magnetic phase transitions and propagation of spin correlations resulting from a quantum quench. The Penning system may also be amenable to observation of spin-liquid behavior thought to arise in systems where the underlying lattice structure can frustrate long-range ordering. Supported by DARPA OLE and NIST.

Shearlet-based measures of entropy and complexity for two-dimensional patterns

NASA Astrophysics Data System (ADS)

Brazhe, Alexey

2018-06-01

New spatial entropy and complexity measures for two-dimensional patterns are proposed. The approach is based on the notion of disequilibrium and is built on statistics of directional multiscale coefficients of the fast finite shearlet transform. Shannon entropy and Jensen-Shannon divergence measures are employed. Both local and global spatial complexity and entropy estimates can be obtained, thus allowing for spatial mapping of complexity in inhomogeneous patterns. The algorithm is validated in numerical experiments with a gradually decaying periodic pattern and Ising surfaces near critical state. It is concluded that the proposed algorithm can be instrumental in describing a wide range of two-dimensional imaging data, textures, or surfaces, where an understanding of the level of order or randomness is desired.

Ising model of cardiac thin filament activation with nearest-neighbor cooperative interactions

NASA Technical Reports Server (NTRS)

Rice, John Jeremy; Stolovitzky, Gustavo; Tu, Yuhai; de Tombe, Pieter P.; Bers, D. M. (Principal Investigator)

2003-01-01

We have developed a model of cardiac thin filament activation using an Ising model approach from equilibrium statistical physics. This model explicitly represents nearest-neighbor interactions between 26 troponin/tropomyosin units along a one-dimensional array that represents the cardiac thin filament. With transition rates chosen to match experimental data, the results show that the resulting force-pCa (F-pCa) relations are similar to Hill functions with asymmetries, as seen in experimental data. Specifically, Hill plots showing (log(F/(1-F)) vs. log [Ca]) reveal a steeper slope below the half activation point (Ca(50)) compared with above. Parameter variation studies show interplay of parameters that affect the apparent cooperativity and asymmetry in the F-pCa relations. The model also predicts that Ca binding is uncooperative for low [Ca], becomes steeper near Ca(50), and becomes uncooperative again at higher [Ca]. The steepness near Ca(50) mirrors the steep F-pCa as a result of thermodynamic considerations. The model also predicts that the correlation between troponin/tropomyosin units along the one-dimensional array quickly decays at high and low [Ca], but near Ca(50), high correlation occurs across the whole array. This work provides a simple model that can account for the steepness and shape of F-pCa relations that other models fail to reproduce.

Entropy production in a Glauber–Ising irreversible model with dynamical competition

NASA Astrophysics Data System (ADS)

Barbosa, Oscar A.; Tomé, Tânia

2018-06-01

An out of equilibrium Glauber–Ising model, evolving in accordance with an irreversible and stochastic Markovian dynamics, is analyzed in order to improve our comprehension concerning critical behavior and phase transitions in nonequilibrium systems. Therefore, a lattice model ruled by the competition between two Glauber dynamics acting on interlaced square lattices is proposed. Previous results have shown how the entropy production provides information about irreversibility and criticality. Mean-field approximations and Monte Carlo simulations were used in the analysis. The results obtained here show a continuous phase transition, reflected in the entropy production as a logarithmic divergence of its derivative, which suggests a shared universality class with the irreversible models invariant under the symmetry operations of the Ising model.

RG flow from Φ 4 theory to the 2D Ising model

DOE PAGES

Anand, Nikhil; Genest, Vincent X.; Katz, Emanuel; ...

2017-08-16

We study 1+1 dimensional Φ 4 theory using the recently proposed method of conformal truncation. Starting in the UV CFT of free field theory, we construct a complete basis of states with definite conformal Casimir, C. We use these states to express the Hamiltonian of the full interacting theory in lightcone quantization. After truncating to states with C≤C max, we numerically diagonalize the Hamiltonian at strong coupling and study the resulting IR dynamics. We compute non-perturbative spectral densities of several local operators, which are equivalent to real-time, infinite-volume correlation functions. These spectral densities, which include the Zamolodchikov C-function along themore » full RG flow, are calculable at any value of the coupling. Near criticality, our numerical results reproduce correlation functions in the 2D Ising model.« less

Unconventional quantum antiferromagnetism with a fourfold symmetry breaking in a spin-1/2 Ising-Heisenberg pentagonal chain

NASA Astrophysics Data System (ADS)

Karľová, Katarína; Strečka, Jozef; Lyra, Marcelo L.

2018-03-01

The spin-1/2 Ising-Heisenberg pentagonal chain is investigated with use of the star-triangle transformation, which establishes a rigorous mapping equivalence with the effective spin-1/2 Ising zigzag ladder. The investigated model has a rich ground-state phase diagram including two spectacular quantum antiferromagnetic ground states with a fourfold broken symmetry. It is demonstrated that these long-period quantum ground states arise due to a competition between the effective next-nearest-neighbor and nearest-neighbor interactions of the corresponding spin-1/2 Ising zigzag ladder. The concurrence is used to quantify the bipartite entanglement between the nearest-neighbor Heisenberg spin pairs, which are quantum-mechanically entangled in two quantum ground states with or without spontaneously broken symmetry. The pair correlation functions between the nearest-neighbor Heisenberg spins as well as the next-nearest-neighbor and nearest-neighbor Ising spins were investigated with the aim to bring insight into how a relevant short-range order manifests itself at low enough temperatures. It is shown that the specific heat displays temperature dependencies with either one or two separate round maxima.

Statistical Mechanics of Coherent Ising Machine — The Case of Ferromagnetic and Finite-Loading Hopfield Models —

NASA Astrophysics Data System (ADS)

Aonishi, Toru; Mimura, Kazushi; Utsunomiya, Shoko; Okada, Masato; Yamamoto, Yoshihisa

2017-10-01

The coherent Ising machine (CIM) has attracted attention as one of the most effective Ising computing architectures for solving large scale optimization problems because of its scalability and high-speed computational ability. However, it is difficult to implement the Ising computation in the CIM because the theories and techniques of classical thermodynamic equilibrium Ising spin systems cannot be directly applied to the CIM. This means we have to adapt these theories and techniques to the CIM. Here we focus on a ferromagnetic model and a finite loading Hopfield model, which are canonical models sharing a common mathematical structure with almost all other Ising models. We derive macroscopic equations to capture nonequilibrium phase transitions in these models. The statistical mechanical methods developed here constitute a basis for constructing evaluation methods for other Ising computation models.

Universality, twisted fans, and the Ising model. [Renormalization, two-loop calculations, scale

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dash, J.W.; Harrington, S.J.

1975-06-24

Critical exponents are evaluated for the Ising model using universality in the form of ''twisted fans'' previously introduced in Reggeon field theory. The universality is with respect to scales induced through renormalization. Exact twists are obtained at ..beta.. = 0 in one loop for D = 2,3 with ..nu.. = 0.75 and 0.60 respectively. In two loops one obtains ..nu.. approximately 1.32 and 0.68. No twists are obtained for eta, however. The results for the standard two loop calculations are also presented as functions of a scale.

Investigation of phase diagrams for cylindrical Ising nanotube using cellular automata

NASA Astrophysics Data System (ADS)

Astaraki, M.; Ghaemi, M.; Afzali, K.

2018-05-01

Recent developments in the field of applied nanoscience and nanotechnology have heightened the need for categorizing various characteristics of nanostructures. In this regard, this paper establishes a novel method to investigate magnetic properties (phase diagram and spontaneous magnetization) of a cylindrical Ising nanotube. Using a two-layer Ising model and the core-shell concept, the interactions within nanotube has been modelled. In the model, both ferromagnetic and antiferromagnetic cases have been considered. Furthermore, the effect of nanotube's length on the critical temperature is investigated. The model has been simulated using cellular automata approach and phase diagrams were constructed for different values of inter- and intra-layer couplings. For the antiferromagnetic case, the possibility of existence of compensation point is observed.

Ground-state magnetization of the Ising spin glass: A recursive numerical method and Chen-Ma scaling

NASA Astrophysics Data System (ADS)

Sepehrinia, Reza; Chalangari, Fartash

2018-03-01

The ground-state properties of quasi-one-dimensional (Q1D) Ising spin glass are investigated using an exact numerical approach and analytical arguments. A set of coupled recursive equations for the ground-state energy are introduced and solved numerically. For various types of coupling distribution, we obtain accurate results for magnetization, particularly in the presence of a weak external magnetic field. We show that in the weak magnetic field limit, similar to the 1D model, magnetization exhibits a singular power-law behavior with divergent susceptibility. Remarkably, the spectrum of magnetic exponents is markedly different from that of the 1D system even in the case of two coupled chains. The magnetic exponent makes a crossover from being dependent on a distribution function to a constant value independent of distribution. We provide an analytic theory for these observations by extending the Chen-Ma argument to the Q1D case. We derive an analytical formula for the exponent which is in perfect agreement with the numerical results.

Order by disorder and gaugelike degeneracy in a quantum pyrochlore antiferromagnet.

PubMed

Henley, Christopher L

2006-02-03

The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg spins of large spin length S is a highly frustrated model with a macroscopic degeneracy of classical ground states. The zero-point energy of (harmonic-order) spin-wave fluctuations distinguishes a subset of these states. I derive an approximate but illuminating effective Hamiltonian, acting within the subspace of Ising spin configurations representing the collinear ground states. It consists of products of Ising spins around loops, i.e., has the form of a Z2 lattice gauge theory. The remaining ground-state entropy is still infinite but not extensive, being O(L) for system size O(L3). All these ground states have unit cells bigger than those considered previously.

Relations between dissipated work and Rényi divergences in the generalized Gibbs ensemble

NASA Astrophysics Data System (ADS)

Wei, Bo-Bo

2018-04-01

In this work, we show that the dissipation in a many-body system under an arbitrary nonequilibrium process is related to the Rényi divergences between two states along the forward and reversed dynamics under a very general family of initial conditions. This relation generalizes the links between dissipated work and Rényi divergences to quantum systems with conserved quantities whose equilibrium state is described by the generalized Gibbs ensemble. The relation is applicable for quantum systems with conserved quantities and can be applied to protocols driving the system between integrable and chaotic regimes. We demonstrate our ideas by considering the one-dimensional transverse quantum Ising model and the Jaynes-Cummings model which are driven out of equilibrium.

Loop optimization for tensor network renormalization

NASA Astrophysics Data System (ADS)

Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.

Block voter model: Phase diagram and critical behavior

NASA Astrophysics Data System (ADS)

Sampaio-Filho, C. I. N.; Moreira, F. G. B.

2011-11-01

We introduce and study the block voter model with noise on two-dimensional square lattices using Monte Carlo simulations and finite-size scaling techniques. The model is defined by an outflow dynamics where a central set of NPCS spins, here denoted by persuasive cluster spins (PCS), tries to influence the opinion of their neighboring counterparts. We consider the collective behavior of the entire system with varying PCS size. When NPCS>2, the system exhibits an order-disorder phase transition at a critical noise parameter qc which is a monotonically increasing function of the size of the persuasive cluster. We conclude that a larger PCS has more power of persuasion, when compared to a smaller one. It also seems that the resulting critical behavior is Ising-like independent of the range of interaction.

Linking market interaction intensity of 3D Ising type financial model with market volatility

NASA Astrophysics Data System (ADS)

Fang, Wen; Ke, Jinchuan; Wang, Jun; Feng, Ling

2016-11-01

Microscopic interaction models in physics have been used to investigate the complex phenomena of economic systems. The simple interactions involved can lead to complex behaviors and help the understanding of mechanisms in the financial market at a systemic level. This article aims to develop a financial time series model through 3D (three-dimensional) Ising dynamic system which is widely used as an interacting spins model to explain the ferromagnetism in physics. Through Monte Carlo simulations of the financial model and numerical analysis for both the simulation return time series and historical return data of Hushen 300 (HS300) index in Chinese stock market, we show that despite its simplicity, this model displays stylized facts similar to that seen in real financial market. We demonstrate a possible underlying link between volatility fluctuations of real stock market and the change in interaction strengths of market participants in the financial model. In particular, our stochastic interaction strength in our model demonstrates that the real market may be consistently operating near the critical point of the system.

Probability distribution of the entanglement across a cut at an infinite-randomness fixed point

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Majumdar, Satya N.; Huse, David A.

2017-03-01

We calculate the probability distribution of entanglement entropy S across a cut of a finite one-dimensional spin chain of length L at an infinite-randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form p (S |L ) ˜L-ψ (k ) , where k ≡S /ln[L /L0] , the large deviation function ψ (k ) is found explicitly, and L0 is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix-product-state-based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large L via a mapping to Majorana fermions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ko, L.F.

Calculations for the two-point correlation functions in the scaling limit for two statistical models are presented. In Part I, the Ising model with a linear defect is studied for T < T/sub c/ and T > T/sub c/. The transfer matrix method of Onsager and Kaufman is used. The energy-density correlation is given by functions related to the modified Bessel functions. The dispersion expansion for the spin-spin correlation functions are derived. The dominant behavior for large separations at T not equal to T/sub c/ is extracted. It is shown that these expansions lead to systems of Fredholm integral equations. Inmore » Part II, the electric correlation function of the eight-vertex model for T < T/sub c/ is studied. The eight vertex model decouples to two independent Ising models when the four spin coupling vanishes. To first order in the four-spin coupling, the electric correlation function is related to a three-point function of the Ising model. This relation is systematically investigated and the full dispersion expansion (to first order in four-spin coupling) is obtained. The results is a new kind of structure which, unlike those of many solvable models, is apparently not expressible in terms of linear integral equations.« less

Inverse Ising problem in continuous time: A latent variable approach

NASA Astrophysics Data System (ADS)

Donner, Christian; Opper, Manfred

2017-12-01

We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.

Exploring Replica-Exchange Wang-Landau sampling in higher-dimensional parameter space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Valentim, Alexandra; Rocha, Julio C. S.; Tsai, Shan-Ho

We considered a higher-dimensional extension for the replica-exchange Wang-Landau algorithm to perform a random walk in the energy and magnetization space of the two-dimensional Ising model. This hybrid scheme combines the advantages of Wang-Landau and Replica-Exchange algorithms, and the one-dimensional version of this approach has been shown to be very efficient and to scale well, up to several thousands of computing cores. This approach allows us to split the parameter space of the system to be simulated into several pieces and still perform a random walk over the entire parameter range, ensuring the ergodicity of the simulation. Previous work, inmore » which a similar scheme of parallel simulation was implemented without using replica exchange and with a different way to combine the result from the pieces, led to discontinuities in the final density of states over the entire range of parameters. From our simulations, it appears that the replica-exchange Wang-Landau algorithm is able to overcome this diculty, allowing exploration of higher parameter phase space by keeping track of the joint density of states.« less

Direct imaging of coexisting ordered and frustrated sublattices in artificial ferromagnetic quasicrystals

DOE PAGES

Farmer, B.; Bhat, V. S.; Balk, A.; ...

2016-04-25

Here, we have used scanning electron microscopy with polarization analysis and photoemission electron microscopy to image the two-dimensional magnetization of permalloy films patterned into Penrose P2 tilings (P2T). The interplay of exchange interactions in asymmetrically coordinated vertices and short-range dipole interactions among connected film segments stabilize magnetically ordered, spatially distinct sublattices that coexist with frustrated sublattices at room temperature. Numerical simulations that include long-range dipole interactions between sublattices agree with images of as-grown P2T samples and predict a magnetically ordered ground state for a two-dimensional quasicrystal lattice of classical Ising spins.

Nonequilibrium magnetic properties in a two-dimensional kinetic mixed Ising system within the effective-field theory and Glauber-type stochastic dynamics approach.

PubMed

Ertaş, Mehmet; Deviren, Bayram; Keskin, Mustafa

2012-11-01

Nonequilibrium magnetic properties in a two-dimensional kinetic mixed spin-2 and spin-5/2 Ising system in the presence of a time-varying (sinusoidal) magnetic field are studied within the effective-field theory (EFT) with correlations. The time evolution of the system is described by using Glauber-type stochastic dynamics. The dynamic EFT equations are derived by employing the Glauber transition rates for two interpenetrating square lattices. We investigate the time dependence of the magnetizations for different interaction parameter values in order to find the phases in the system. We also study the thermal behavior of the dynamic magnetizations, the hysteresis loop area, and dynamic correlation. The dynamic phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane and we observe that the system exhibits dynamic tricritical and reentrant behaviors. Moreover, the system also displays a double critical end point (B), a zero-temperature critical point (Z), a critical end point (E), and a triple point (TP). We also performed a comparison with the mean-field prediction in order to point out the effects of correlations and found that some of the dynamic first-order phase lines, which are artifacts of the mean-field approach, disappeared.

Herding, minority game, market clearing and efficient markets in a simple spin model framework

NASA Astrophysics Data System (ADS)

Kristoufek, Ladislav; Vosvrda, Miloslav

2018-01-01

We present a novel approach towards the financial Ising model. Most studies utilize the model to find settings which generate returns closely mimicking the financial stylized facts such as fat tails, volatility clustering and persistence, and others. We tackle the model utility from the other side and look for the combination of parameters which yields return dynamics of the efficient market in the view of the efficient market hypothesis. Working with the Ising model, we are able to present nicely interpretable results as the model is based on only two parameters. Apart from showing the results of our simulation study, we offer a new interpretation of the Ising model parameters via inverse temperature and entropy. We show that in fact market frictions (to a certain level) and herding behavior of the market participants do not go against market efficiency but what is more, they are needed for the markets to be efficient.

Accurate Mapping of Multilevel Rydberg Atoms on Interacting Spin-1 /2 Particles for the Quantum Simulation of Ising Models

NASA Astrophysics Data System (ADS)

de Léséleuc, Sylvain; Weber, Sebastian; Lienhard, Vincent; Barredo, Daniel; Büchler, Hans Peter; Lahaye, Thierry; Browaeys, Antoine

2018-03-01

We study a system of atoms that are laser driven to n D3 /2 Rydberg states and assess how accurately they can be mapped onto spin-1 /2 particles for the quantum simulation of anisotropic Ising magnets. Using nonperturbative calculations of the pair potentials between two atoms in the presence of electric and magnetic fields, we emphasize the importance of a careful selection of experimental parameters in order to maintain the Rydberg blockade and avoid excitation of unwanted Rydberg states. We benchmark these theoretical observations against experiments using two atoms. Finally, we show that in these conditions, the experimental dynamics observed after a quench is in good agreement with numerical simulations of spin-1 /2 Ising models in systems with up to 49 spins, for which numerical simulations become intractable.

Effect of increasing disorder on domains of the 2d Coulomb glass.

PubMed

Bhandari, Preeti; Malik, Vikas

2017-12-06

We have studied a two dimensional lattice model of Coulomb glass for a wide range of disorders at [Formula: see text]. The system was first annealed using Monte Carlo simulation. Further minimization of the total energy of the system was done using an algorithm developed by Baranovskii et al, followed by cluster flipping to obtain the pseudo-ground states. We have shown that the energy required to create a domain of linear size L in d dimensions is proportional to [Formula: see text]. Using Imry-Ma arguments given for random field Ising model, one gets critical dimension [Formula: see text] for Coulomb glass. The investigation of domains in the transition region shows a discontinuity in staggered magnetization which is an indication of a first-order type transition from charge-ordered phase to disordered phase. The structure and nature of random field fluctuations of the second largest domain in Coulomb glass are inconsistent with the assumptions of Imry and Ma, as was also reported for random field Ising model. The study of domains showed that in the transition region there were mostly two large domains, and that as disorder was increased the two large domains remained, but a large number of small domains also opened up. We have also studied the properties of the second largest domain as a function of disorder. We furthermore analysed the effect of disorder on the density of states, and showed a transition from hard gap at low disorders to a soft gap at higher disorders. At [Formula: see text], we have analysed the soft gap in detail, and found that the density of states deviates slightly ([Formula: see text]) from the linear behaviour in two dimensions. Analysis of local minima show that the pseudo-ground states have similar structure.

Phase transition in 2-d system of quadrupoles on square lattice with anisotropic field

NASA Astrophysics Data System (ADS)

Sallabi, A. K.; Alkhttab, M.

2014-12-01

Monte Carlo method is used to study a simple model of two-dimensional interacting quadrupoles on ionic square lattice with anisotropic strength provided by the ionic lattice. Order parameter, susceptibility and correlation function data, show that this system form an ordered structure with p(2×1) symmetry at low temperature. The p(2×1) structure undergoes an order-disorder phase transition into disordered (1×1) phase at 8.3K. The two-point correlation function show exponential dependence on distance both above and below the transition temperature. At Tc the two-point correlation function shows a power law dependence on distance, e.g. C(r) ~ 1η. The value of the exponent η at Tc shows small deviation from the Ising value and indicates that this system falls into the same universality class as the XY model with cubic anisotropy. This model can be applied to prototypical quadrupoles physisorbed systems as N2 on NaCl(100).

Entanglement in the Anisotropic Kondo Necklace Model

NASA Astrophysics Data System (ADS)

Mendoza-Arenas, J. J.; Franco, R.; Silva-Valencia, J.

We study the entanglement in the one-dimensional Kondo necklace model with exact diagonalization, calculating the concurrence as a function of the Kondo coupling J and an anisotropy η in the interaction between conduction spins, and we review some results previously obtained in the limiting cases η = 0 and 1. We observe that as J increases, localized and conduction spins get more entangled, while neighboring conduction spins diminish their concurrence; localized spins require a minimum concurrence between conduction spins to be entangled. The anisotropy η diminishes the entanglement for neighboring spins when it increases, driving the system to the Ising limit η = 1 where conduction spins are not entangled. We observe that the concurrence does not give information about the quantum phase transition in the anisotropic Kondo necklace model (between a Kondo singlet and an antiferromagnetic state), but calculating the von Neumann block entropy with the density matrix renormalization group in a chain of 100 sites for the Ising limit indicates that this quantity is useful for locating the quantum critical point.

Two-dimensional Magnetism in Arrays of Superconducting Rings

NASA Astrophysics Data System (ADS)

Reich, Daniel H.

1996-03-01

An array of superconducting rings in an applied field corresponding to a flux of Φ0 /2 per ring behaves like a 2D Ising antiferromagnet. Each ring has two energetically equivalent states with equal and opposite magnetic moments due to fluxoid quantization, and the dipolar coupling between rings favors antiparallel alignment of the moments. Using SQUID magnetometry and scanning Hall probe microscopy, we have studied the dynamics and magnetic configurations of micron-size aluminum rings on square, triangular, honeycomb, and kagomé lattices. We have found that there are significant antiferromagnetic correlations between rings, and that effects of geometrical frustration can be observed on the triangular and kagomé lattices. Long range correlations on the other lattices are suppressed by the analog of spin freezing that locks the rings in metastable states at low temperatures, and by quenched disorder due to imperfections in the fabrication. This disorder produces a roughly 1% variation in the rings' areas, which translates into an effective random field on the spins. The ring arrays are thus an extremely good realization of the 2D random-field Ising model. (Performed in collaboration with D. Davidović, S. Kumar, J. Siegel, S. B. Field, R. C. Tiberio, R. Hey, and K. Ploog.) (Supported by NSF grants DMR-9222541, and DMR-9357518, and by the David and Lucile Packard Foundation.)

Emergent order in the kagome Ising magnet Dy3Mg2Sb3O14

PubMed Central

Paddison, Joseph A. M.; Ong, Harapan S.; Hamp, James O.; Mukherjee, Paromita; Bai, Xiaojian; Tucker, Matthew G.; Butch, Nicholas P.; Castelnovo, Claudio; Mourigal, Martin; Dutton, S. E.

2016-01-01

The Ising model—in which degrees of freedom (spins) are binary valued (up/down)—is a cornerstone of statistical physics that shows rich behaviour when spins occupy a highly frustrated lattice such as kagome. Here we show that the layered Ising magnet Dy3Mg2Sb3O14 hosts an emergent order predicted theoretically for individual kagome layers of in-plane Ising spins. Neutron-scattering and bulk thermomagnetic measurements reveal a phase transition at ∼0.3 K from a disordered spin-ice-like regime to an emergent charge ordered state, in which emergent magnetic charge degrees of freedom exhibit three-dimensional order while spins remain partially disordered. Monte Carlo simulations show that an interplay of inter-layer interactions, spin canting and chemical disorder stabilizes this state. Our results establish Dy3Mg2Sb3O14 as a tuneable system to study interacting emergent charges arising from kagome Ising frustration. PMID:27996012

Importance of positive feedbacks and overconfidence in a self-fulfilling Ising model of financial markets

NASA Astrophysics Data System (ADS)

Sornette, Didier; Zhou, Wei-Xing

2006-10-01

Following a long tradition of physicists who have noticed that the Ising model provides a general background to build realistic models of social interactions, we study a model of financial price dynamics resulting from the collective aggregate decisions of agents. This model incorporates imitation, the impact of external news and private information. It has the structure of a dynamical Ising model in which agents have two opinions (buy or sell) with coupling coefficients, which evolve in time with a memory of how past news have explained realized market returns. We study two versions of the model, which differ on how the agents interpret the predictive power of news. We show that the stylized facts of financial markets are reproduced only when agents are overconfident and mis-attribute the success of news to predict return to herding effects, thereby providing positive feedbacks leading to the model functioning close to the critical point. Our model exhibits a rich multifractal structure characterized by a continuous spectrum of exponents of the power law relaxation of endogenous bursts of volatility, in good agreement with previous analytical predictions obtained with the multifractal random walk model and with empirical facts.

The structural phase diagram and oxygen equilibrium partial pressure of YBa 2Cu 3O 6+ x studied by neutron powder diffraction and gas volumetry

NASA Astrophysics Data System (ADS)

Andersen, N. H.; Lebech, B.; Poulsen, H. F.

1990-12-01

An experimental technique based on neutron powder diffraction and gas volumetry is presented and used to study the structural phase diagram of YBa 2Cu 3O 6+ x under equilibrium conditions in an extended part of ( x, T)-phase (0.15< x<0.92 and 25° C< T<725°C). Our experimental observations lend strong support to a recent two-dimensional anisotropic next-nearest-neighbour Ising model calculation (the ASYNNNI model) of the basal plane oxygen ordering based of first principle interaction parameters. Simultaneous measurements of the oxygen equilibrium partial pressure show anomalies, one of which proves the thermodynamic stability of the orthorhombic OII double cell structure. Striking similarity with predictions of recent model calculations support that another anomaly may be interpreted to result from local one-dimensional fluctuations in the distribution of oxygen atoms in the basal plane of tetragonal YBCO. Our pressure data also indicate that x=0.92 is a maximum obtainable oxygen concentration for oxygen pressures below 760 Torr.

Heat conduction in one-dimensional aperiodic quantum Ising chains.

PubMed

Li, Wenjuan; Tong, Peiqing

2011-03-01

The heat conductivity of nonperiodic quantum Ising chains whose ends are connected with heat baths at different temperatures are studied numerically by solving the Lindblad master equation. The chains are subjected to a uniform transverse field h, while the exchange coupling J{m} between the nearest-neighbor spins takes the two values J{A} and J{B} arranged in Fibonacci, generalized Fibonacci, Thue-Morse, and period-doubling sequences. We calculate the energy-density profile and energy current of the resulting nonequilibrium steady states to study the heat-conducting behavior of finite but large systems. Although these nonperiodic quantum Ising chains are integrable, it is clearly found that energy gradients exist in all chains and the energy currents appear to scale as the system size ~N{α}. By increasing the ratio of couplings, the exponent α can be modulated from α > -1 to α < -1 corresponding to the nontrivial transition from the abnormal heat transport to the heat insulator. The influences of the temperature gradient and the magnetic field to heat conduction have also been discussed.

Dynamic Transition and Resonance in Coupled Oscillators Under Symmetry-Breaking Fields

NASA Astrophysics Data System (ADS)

Choi, J.; Choi, M. Y.; Chung, M. S.; Yoon, B.-G.

2013-06-01

We investigate numerically the dynamic properties of a system of globally coupled oscillators driven by periodic symmetry-breaking fields in the presence of noise. The phase distribution of the oscillators is computed and a dynamic transition is disclosed. It is further found that the stochastic resonance is closely related to the behavior of the dynamic order parameter, which is in turn explained by the formation of a bi-cluster in the system. Here noise tends to symmetrize the motion of the oscillators, facilitating the bi-cluster formation. The observed resonance appears to be of the same class as the resonance present in the two-dimensional Ising model under oscillating fields.

Local and nonlocal order parameters in the Kitaev chain

NASA Astrophysics Data System (ADS)

Chitov, Gennady Y.

2018-02-01

We have calculated order parameters for the phases of the Kitaev chain with interaction and dimerization at a special symmetric point applying the Jordan-Wigner and other duality transformations. We use string order parameters (SOPs) defined via the correlation functions of the Majorana string operators. The SOPs are mapped onto the local order parameters of some dual Hamiltonians and easily calculated. We have shown that the phase diagram of the interacting dimerized chain comprises the phases with the conventional local order as well as the phases with nonlocal SOPs. From the results for the critical indices, we infer the two-dimensional Ising universality class of criticality at the particular symmetry point where the model is exactly solvable.

Thermodynamically self-consistent theory for the Blume-Capel model.

PubMed

Grollau, S; Kierlik, E; Rosinberg, M L; Tarjus, G

2001-04-01

We use a self-consistent Ornstein-Zernike approximation to study the Blume-Capel ferromagnet on three-dimensional lattices. The correlation functions and the thermodynamics are obtained from the solution of two coupled partial differential equations. The theory provides a comprehensive and accurate description of the phase diagram in all regions, including the wing boundaries in a nonzero magnetic field. In particular, the coordinates of the tricritical point are in very good agreement with the best estimates from simulation or series expansion. Numerical and analytical analysis strongly suggest that the theory predicts a universal Ising-like critical behavior along the lambda line and the wing critical lines, and a tricritical behavior governed by mean-field exponents.

Overcoming the sign problem at finite temperature: Quantum tensor network for the orbital eg model on an infinite square lattice

NASA Astrophysics Data System (ADS)

Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.

2017-07-01

The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied to a model suffering the notorious quantum Monte Carlo sign problem—the orbital eg model with spatially highly anisotropic orbital interactions. Coarse graining of the tensor network along the inverse temperature β yields a numerically tractable 2D tensor network representing the Gibbs state. Its bond dimension D —limiting the amount of entanglement—is a natural refinement parameter. Increasing D we obtain a converged order parameter and its linear susceptibility close to the critical point. They confirm the existence of finite order parameter below the critical temperature Tc, provide a numerically exact estimate of Tc, and give the critical exponents within 1 % of the 2D Ising universality class.

Evolutionary games combining two or three pair coordinations on a square lattice

NASA Astrophysics Data System (ADS)

Király, Balázs; Szabó, György

2017-10-01

We study multiagent logit-rule-driven evolutionary games on a square lattice whose pair interactions are composed of a maximal number of nonoverlapping elementary coordination games describing Ising-type interactions between just two of the available strategies. Using Monte Carlo simulations we investigate the macroscopic noise-level-dependent behavior of the two- and three-pair games and the critical properties of the continuous phase transtitions these systems exhibit. The four-strategy game is shown to be equivalent to a system that consists of two independent and identical Ising models.

Evolutionary games combining two or three pair coordinations on a square lattice.

PubMed

Király, Balázs; Szabó, György

2017-10-01

We study multiagent logit-rule-driven evolutionary games on a square lattice whose pair interactions are composed of a maximal number of nonoverlapping elementary coordination games describing Ising-type interactions between just two of the available strategies. Using Monte Carlo simulations we investigate the macroscopic noise-level-dependent behavior of the two- and three-pair games and the critical properties of the continuous phase transtitions these systems exhibit. The four-strategy game is shown to be equivalent to a system that consists of two independent and identical Ising models.

Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories.

PubMed

Buican, Matthew; Laczko, Zoltan

2018-02-23

In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N=2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.

Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories

NASA Astrophysics Data System (ADS)

Buican, Matthew; Laczko, Zoltan

2018-02-01

In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N =2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N =2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.

Quantum transverse-field Ising model on an infinite tree from matrix product states

NASA Astrophysics Data System (ADS)

Nagaj, Daniel; Farhi, Edward; Goldstone, Jeffrey; Shor, Peter; Sylvester, Igor

2008-06-01

We give a generalization to an infinite tree geometry of Vidal’s infinite time-evolving block decimation (iTEBD) algorithm [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)] for simulating an infinite line of quantum spins. We numerically investigate the quantum Ising model in a transverse field on the Bethe lattice using the matrix product state ansatz. We observe a second order phase transition, with certain key differences from the transverse field Ising model on an infinite spin chain. We also investigate a transverse field Ising model with a specific longitudinal field. When the transverse field is turned off, this model has a highly degenerate ground state as opposed to the pure Ising model whose ground state is only doubly degenerate.

Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction

DOE PAGES

Chan, Yang-Hao; Jin, Wen; Jiang, Hong-Chen; ...

2017-12-29

We report a combined analytical and density matrix renormalized group study of the antiferromagnetic XXZ spin-1/2 Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya (DM) interaction and a transverse magnetic eld. The numerically determined phase diagram of this model, which features two ordered Ising phases and a critical Luttinger liquid one with fully broken spin-rotational symmetry, agrees well with the predictions of Garate and Affleck [Phys. Rev. B 81, 144419 (2010)]. We also con rm the prevalence of the Nz Neel Ising order in the regime of comparable DM and magnetic field magnitudes.

Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chan, Yang-Hao; Jin, Wen; Jiang, Hong-Chen

We report a combined analytical and density matrix renormalized group study of the antiferromagnetic XXZ spin-1/2 Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya (DM) interaction and a transverse magnetic eld. The numerically determined phase diagram of this model, which features two ordered Ising phases and a critical Luttinger liquid one with fully broken spin-rotational symmetry, agrees well with the predictions of Garate and Affleck [Phys. Rev. B 81, 144419 (2010)]. We also con rm the prevalence of the Nz Neel Ising order in the regime of comparable DM and magnetic field magnitudes.

The magnetisation distribution of the Ising model - a new approach

NASA Astrophysics Data System (ADS)

Hakan Lundow, Per; Rosengren, Anders

2010-03-01

A completely new approach to the Ising model in 1 to 5 dimensions is developed. We employ a generalisation of the binomial coefficients to describe the magnetisation distributions of the Ising model. For the complete graph this distribution is exact. For simple lattices of dimensions d=1 and d=5 the magnetisation distributions are remarkably well-fitted by the generalized binomial distributions. For d=4 we are only slightly less successful, while for d=2,3 we see some deviations (with exceptions!) between the generalized binomial and the Ising distribution. The results speak in favour of the generalized binomial distribution's correctness regarding their general behaviour in comparison to the Ising model. A theoretical analysis of the distribution's moments also lends support their being correct asymptotically, including the logarithmic corrections in d=4. The full extent to which they correctly model the Ising distribution, and for which graph families, is not settled though.

Self-organized critical behavior and marginality in Ising spin glasses

NASA Astrophysics Data System (ADS)

Sharma, Auditya; Yeo, Joonhyun; Moore, M. A.

2018-05-01

We have studied numerically the states reached in a quench from various temperatures in the one-dimensional fully-connected Kotliar, Anderson and Stein Ising spin glass model. This is a model where there are long-range interactions between the spins which falls off as a power σ of their separation. We have made a detailed study in particular of the energies of the states reached in a quench from infinite temperature and their overlaps, including the spin glass susceptibility. In the regime where , where the model is similar to the Sherrington–Kirkpatrick model, we find that the spin glass susceptibility diverges logarithmically with increasing N, the number of spins in the system, whereas for it remains finite. We attribute the behavior for to self-organized critical behavior, where the system after the quench is close to the transition between states which have trivial overlaps and those with the non-trivial overlaps associated with replica symmetry breaking. We have also found by studying the distribution of local fields that the states reached in the quench have marginal stability but only when .

Boson-mediated quantum spin simulators in transverse fields: X Y model and spin-boson entanglement

NASA Astrophysics Data System (ADS)

Wall, Michael L.; Safavi-Naini, Arghavan; Rey, Ana Maria

2017-01-01

The coupling of spins to long-wavelength bosonic modes is a prominent means to engineer long-range spin-spin interactions, and has been realized in a variety of platforms, such as atoms in optical cavities and trapped ions. To date, much of the experimental focus has been on the realization of long-range Ising models, but generalizations to other spin models are highly desirable. In this work, we explore a previously unappreciated connection between the realization of an X Y model by off-resonant driving of a single sideband of boson excitation (i.e., a single-beam Mølmer-Sørensen scheme) and a boson-mediated Ising simulator in the presence of a transverse field. In particular, we show that these two schemes have the same effective Hamiltonian in suitably defined rotating frames, and analyze the emergent effective X Y spin model through a truncated Magnus series and numerical simulations. In addition to X Y spin-spin interactions that can be nonperturbatively renormalized from the naive Ising spin-spin coupling constants, we find an effective transverse field that is dependent on the thermal energy of the bosons, as well as other spin-boson couplings that cause spin-boson entanglement not to vanish at any time. In the case of a boson-mediated Ising simulator with transverse field, we discuss the crossover from transverse field Ising-like to X Y -like spin behavior as a function of field strength.

Ab initio optimization principle for the ground states of translationally invariant strongly correlated quantum lattice models.

PubMed

Ran, Shi-Ju

2016-05-01

In this work, a simple and fundamental numeric scheme dubbed as ab initio optimization principle (AOP) is proposed for the ground states of translational invariant strongly correlated quantum lattice models. The idea is to transform a nondeterministic-polynomial-hard ground-state simulation with infinite degrees of freedom into a single optimization problem of a local function with finite number of physical and ancillary degrees of freedom. This work contributes mainly in the following aspects: (1) AOP provides a simple and efficient scheme to simulate the ground state by solving a local optimization problem. Its solution contains two kinds of boundary states, one of which play the role of the entanglement bath that mimics the interactions between a supercell and the infinite environment, and the other gives the ground state in a tensor network (TN) form. (2) In the sense of TN, a novel decomposition named as tensor ring decomposition (TRD) is proposed to implement AOP. Instead of following the contraction-truncation scheme used by many existing TN-based algorithms, TRD solves the contraction of a uniform TN in an opposite way by encoding the contraction in a set of self-consistent equations that automatically reconstruct the whole TN, making the simulation simple and unified; (3) AOP inherits and develops the ideas of different well-established methods, including the density matrix renormalization group (DMRG), infinite time-evolving block decimation (iTEBD), network contractor dynamics, density matrix embedding theory, etc., providing a unified perspective that is previously missing in this fields. (4) AOP as well as TRD give novel implications to existing TN-based algorithms: A modified iTEBD is suggested and the two-dimensional (2D) AOP is argued to be an intrinsic 2D extension of DMRG that is based on infinite projected entangled pair state. This paper is focused on one-dimensional quantum models to present AOP. The benchmark is given on a transverse Ising chain and 2D classical Ising model, showing the remarkable efficiency and accuracy of the AOP.

Ising model of financial markets with many assets

NASA Astrophysics Data System (ADS)

Eckrot, A.; Jurczyk, J.; Morgenstern, I.

2016-11-01

Many models of financial markets exist, but most of them simulate single asset markets. We study a multi asset Ising model of a financial market. Each agent has two possible actions (buy/sell) for every asset. The agents dynamically adjust their coupling coefficients according to past market returns and external news. This leads to fat tails and volatility clustering independent of the number of assets. We find that a separation of news into different channels leads to sector structures in the cross correlations, similar to those found in real markets.

Simulating the Rayleigh-Taylor instability with the Ising model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ball, Justin R.; Elliott, James B.

2011-08-26

The Ising model, implemented with the Metropolis algorithm and Kawasaki dynamics, makes a system with its own physics, distinct from the real world. These physics are sophisticated enough to model behavior similar to the Rayleigh-Taylor instability and by better understanding these physics, we can learn how to modify the system to better re ect reality. For example, we could add a v x and a v y to each spin and modify the exchange rules to incorporate them, possibly using two body scattering laws to construct a more realistic system.

Radiative corrections to the quark masses in the ferromagnetic Ising and Potts field theories

NASA Astrophysics Data System (ADS)

Rutkevich, Sergei B.

2017-10-01

We consider the Ising Field Theory (IFT), and the 3-state Potts Field Theory (PFT), which describe the scaling limits of the two-dimensional lattice q-state Potts model with q = 2, and q = 3, respectively. At zero magnetic field h = 0, both field theories are integrable away from the critical point, have q degenerate vacua in the ferromagnetic phase, and q (q - 1) particles of the same mass - the kinks interpolating between two different vacua. Application of a weak magnetic field induces confinement of kinks into bound states - the "mesons" (for q = 2 , 3) consisting predominantly of two kinks, and "baryons" (for q = 3), which are essentially the three-kink excitations. The kinks in the confinement regime are also called "the quarks". We review and refine the Form Factor Perturbation Theory (FFPT), adapting it to the analysis of the confinement problem in the limit of small h, and apply it to calculate the corrections to the kink (quark) masses induced by the multi-kink fluctuations caused by the weak magnetic field. It is shown that the subleading third-order ∼h3 correction to the kink mass vanishes in the IFT. The leading second order ∼h2 correction to the kink mass in the 3-state PFT is estimated by truncation the infinite form factor expansion at the first term representing contribution of the two-kink fluctuations into the kink self-energy.

Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns

PubMed Central

Ribeiro, Haroldo V.; Zunino, Luciano; Lenzi, Ervin K.; Santoro, Perseu A.; Mendes, Renio S.

2012-01-01

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to fractal landscapes generated numerically where we compare our measures with the Hurst exponent; liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; 12 characteristic textures of liquid crystals where the different values show that the method can distinguish different phases; and Ising surfaces where our method identified the critical temperature and also proved to be stable. PMID:22916097

Ising model simulation in directed lattices and networks

NASA Astrophysics Data System (ADS)

Lima, F. W. S.; Stauffer, D.

2006-01-01

On directed lattices, with half as many neighbours as in the usual undirected lattices, the Ising model does not seem to show a spontaneous magnetisation, at least for lower dimensions. Instead, the decay time for flipping of the magnetisation follows an Arrhenius law on the square and simple cubic lattice. On directed Barabási-Albert networks with two and seven neighbours selected by each added site, Metropolis and Glauber algorithms give similar results, while for Wolff cluster flipping the magnetisation decays exponentially with time.

Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit

DOE PAGES

Huang, Bevin; Clark, Genevieve; Navarro-Moratalla, Efrén; ...

2017-06-07

Since the celebrated discovery of graphene, the family of two-dimensional (2D) materials has grown to encompass a broad range of electronic properties. Recent additions include spin-valley coupled semiconductors, Ising superconductors that can be tuned into a quantum metal, possible Mott insulators with tunable charge-density waves, and topological semi-metals with edge transport. Despite this progress, there is still no 2D crystal with intrinsic magnetism, which would be useful for many technologies such as sensing, information, and data storage. Theoretically, magnetic order is prohibited in the 2D isotropic Heisenberg model at finite temperatures by the Mermin-Wagner theorem. However, magnetic anisotropy removes thismore » restriction and enables, for instance, the occurrence of 2D Ising ferromagnetism. Here, we use magneto-optical Kerr effect (MOKE) microscopy to demonstrate that monolayer chromium triiodide (CrI 3) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 K is only slightly lower than the 61 K of the bulk crystal, consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phases, showcasing the hallmark thickness dependent physical properties typical of van der Waals crystals. Remarkably, bilayer CrI3 displays suppressed magnetization with a metamagnetic effect, while in trilayer the interlayer ferromagnetism observed in the bulk crystal is restored. Our work creates opportunities for studying magnetism by harnessing the unique features of atomically-thin materials, such as electrical control for realizing magnetoelectronics, and van der Waals engineering for novel interface phenomena.« less

Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Bevin; Clark, Genevieve; Navarro-Moratalla, Efrén

Since the celebrated discovery of graphene, the family of two-dimensional (2D) materials has grown to encompass a broad range of electronic properties. Recent additions include spin-valley coupled semiconductors, Ising superconductors that can be tuned into a quantum metal, possible Mott insulators with tunable charge-density waves, and topological semi-metals with edge transport. Despite this progress, there is still no 2D crystal with intrinsic magnetism, which would be useful for many technologies such as sensing, information, and data storage. Theoretically, magnetic order is prohibited in the 2D isotropic Heisenberg model at finite temperatures by the Mermin-Wagner theorem. However, magnetic anisotropy removes thismore » restriction and enables, for instance, the occurrence of 2D Ising ferromagnetism. Here, we use magneto-optical Kerr effect (MOKE) microscopy to demonstrate that monolayer chromium triiodide (CrI 3) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 K is only slightly lower than the 61 K of the bulk crystal, consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phases, showcasing the hallmark thickness dependent physical properties typical of van der Waals crystals. Remarkably, bilayer CrI3 displays suppressed magnetization with a metamagnetic effect, while in trilayer the interlayer ferromagnetism observed in the bulk crystal is restored. Our work creates opportunities for studying magnetism by harnessing the unique features of atomically-thin materials, such as electrical control for realizing magnetoelectronics, and van der Waals engineering for novel interface phenomena.« less

Networked Ising-Sznajd AR-β Model

NASA Astrophysics Data System (ADS)

Nagao, Tomonori; Ohmiya, Mayumi

2009-09-01

The modified Ising-Sznajd model is studied to clarify the machanism of price formation in the stock market. The conventional Ising-Sznajd model is improved as a small world network with the rewireing probability β(t) which depends on the time. Numerical experiments show that phase transition, regarded as a economical crisis, is inevitable in this model.

Parameter diagnostics of phases and phase transition learning by neural networks

NASA Astrophysics Data System (ADS)

Suchsland, Philippe; Wessel, Stefan

2018-05-01

We present an analysis of neural network-based machine learning schemes for phases and phase transitions in theoretical condensed matter research, focusing on neural networks with a single hidden layer. Such shallow neural networks were previously found to be efficient in classifying phases and locating phase transitions of various basic model systems. In order to rationalize the emergence of the classification process and for identifying any underlying physical quantities, it is feasible to examine the weight matrices and the convolutional filter kernels that result from the learning process of such shallow networks. Furthermore, we demonstrate how the learning-by-confusing scheme can be used, in combination with a simple threshold-value classification method, to diagnose the learning parameters of neural networks. In particular, we study the classification process of both fully-connected and convolutional neural networks for the two-dimensional Ising model with extended domain wall configurations included in the low-temperature regime. Moreover, we consider the two-dimensional XY model and contrast the performance of the learning-by-confusing scheme and convolutional neural networks trained on bare spin configurations to the case of preprocessed samples with respect to vortex configurations. We discuss these findings in relation to similar recent investigations and possible further applications.

Microscopic Spin Model for the STOCK Market with Attractor Bubbling on Regular and Small-World Lattices

NASA Astrophysics Data System (ADS)

Krawiecki, A.

A multi-agent spin model for changes of prices in the stock market based on the Ising-like cellular automaton with interactions between traders randomly varying in time is investigated by means of Monte Carlo simulations. The structure of interactions has topology of a small-world network obtained from regular two-dimensional square lattices with various coordination numbers by randomly cutting and rewiring edges. Simulations of the model on regular lattices do not yield time series of logarithmic price returns with statistical properties comparable with the empirical ones. In contrast, in the case of networks with a certain degree of randomness for a wide range of parameters the time series of the logarithmic price returns exhibit intermittent bursting typical of volatility clustering. Also the tails of distributions of returns obey a power scaling law with exponents comparable to those obtained from the empirical data.

Bayesian feature selection for high-dimensional linear regression via the Ising approximation with applications to genomics.

PubMed

Fisher, Charles K; Mehta, Pankaj

2015-06-01

Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the number of samples, as is often the case for many genomic datasets. Here, we introduce a new approach--the Bayesian Ising Approximation (BIA)-to rapidly calculate posterior probabilities for feature relevance in L2 penalized linear regression. In the regime where the regression problem is strongly regularized by the prior, we show that computing the marginal posterior probabilities for features is equivalent to computing the magnetizations of an Ising model with weak couplings. Using a mean field approximation, we show it is possible to rapidly compute the feature selection path described by the posterior probabilities as a function of the L2 penalty. We present simulations and analytical results illustrating the accuracy of the BIA on some simple regression problems. Finally, we demonstrate the applicability of the BIA to high-dimensional regression by analyzing a gene expression dataset with nearly 30 000 features. These results also highlight the impact of correlations between features on Bayesian feature selection. An implementation of the BIA in C++, along with data for reproducing our gene expression analyses, are freely available at http://physics.bu.edu/∼pankajm/BIACode. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Quantum Criticality of an Ising-like Spin-1 /2 Antiferromagnetic Chain in a Transverse Magnetic Field

NASA Astrophysics Data System (ADS)

Wang, Zhe; Lorenz, T.; Gorbunov, D. I.; Cong, P. T.; Kohama, Y.; Niesen, S.; Breunig, O.; Engelmayer, J.; Herman, A.; Wu, Jianda; Kindo, K.; Wosnitza, J.; Zherlitsyn, S.; Loidl, A.

2018-05-01

We report on magnetization, sound-velocity, and magnetocaloric-effect measurements of the Ising-like spin-1 /2 antiferromagnetic chain system BaCo2V2O8 as a function of temperature down to 1.3 K and an applied transverse magnetic field up to 60 T. While across the Néel temperature of TN˜5 K anomalies in magnetization and sound velocity confirm the antiferromagnetic ordering transition, at the lowest temperature the field-dependent measurements reveal a sharp softening of sound velocity v (B ) and a clear minimum of temperature T (B ) at B⊥c,3 D=21.4 T , indicating the suppression of the antiferromagnetic order. At higher fields, the T (B ) curve shows a broad minimum at B⊥c=40 T , accompanied by a broad minimum in the sound velocity and a saturationlike magnetization. These features signal a quantum phase transition, which is further characterized by the divergent behavior of the Grüneisen parameter ΓB∝(B -B⊥c)-1. By contrast, around the critical field, the Grüneisen parameter converges as temperature decreases, pointing to a quantum critical point of the one-dimensional transverse-field Ising model.

Anomalously high potentials observed on ISEE

NASA Technical Reports Server (NTRS)

Whipple, E. C.; Krinsky, I. S.; Torbert, R. B.; Olsen, R. C.

1985-01-01

Data from two electric field experiments and from the plasma composition experiment on ISEE-1 are used to show that the spacecraft charged to close to -70 V in sunlight at 0700 UT on March 17, 1978. Data from the electron spectrometer experiment show that there was a potential barrier of -10 to -20 V about the spacecraft during this event. The potential barrier was effective in turning back emitted photoelectrons to the spacecraft. The stringent electrostatic cleanliness specifications imposed on ISEE make the presence of differential charging unlikely. Modeling of this event is required to determine if the barrier was produced by the presence of space charge.

Local characterization of one-dimensional topologically ordered states

NASA Astrophysics Data System (ADS)

Cui, Jian; Amico, Luigi; Fan, Heng; Gu, Mile; Hamma, Alioscia; Vedral, Vlatko

2013-09-01

We consider one-dimensional Hamiltonian systems whose ground states display symmetry-protected topological order. We show that ground states within the topological phase cannot be connected with each other through local operations and classical communication between a bipartition of the system. Our claim is demonstrated by analyzing the entanglement spectrum and Rényi entropies of different physical systems that provide examples for symmetry-protected topological phases. Specifically, we consider the spin-1/2 cluster-Ising model and a class of spin-1 models undergoing quantum phase transitions to the Haldane phase. Our results provide a probe for symmetry-protected topological order. Since the picture holds even at the system's local scale, our analysis can serve as a local experimental test for topological order.

Field-Induced Magnetic Phase Transitions in a Triangular Lattice Antiferromagnet CuFeO 2 up to 14.5 T

NASA Astrophysics Data System (ADS)

Mitsuda, Setsuo; Mase, Motoshi; Prokes, K.; Kitazawa, Hideaki; Katori, H.

2000-11-01

Neutron diffraction studies on a frustrated triangular lattice antiferromagnet (TLA) CuFeO2 have been performed under an applied magnetic field up to 14.5 T. The first-field-induced state was found to be not the commensurate 5-sublattice (↑↑↑↓↓) magnetic state but rather an incommensurate complex helical state reflecting the Heisenberg spin character of orbital singlet Fe3+ magnetic ions. In contrast, the second-field-induced state was found to be the 5-sublattice (↑↑↑↓↓) magnetic state predicted by the two-dimensional (2D) Ising spin TLA model with competing exchange interactions up to the 3rd neighbors.

Dynamic Algorithms for Transition Matrix Generation

NASA Astrophysics Data System (ADS)

Yevick, David; Lee, Yong Hwan

The methods of [D. Yevick, Int. J. Mod. Phys. C, 1650041] for constructing transition matrices are applied to the two dimensional Ising model. Decreasing the system temperature during the acquisition of the matrix elements yields a reasonably precise specific heat curve for a 32x32 spin system for a limited number (50-100M) of realizations. If the system is instead evolved to first higher and then lower energies within a restricted interval that is steadily displaced in energy as the computation proceeds, a modification which permits backward displacements up to a certain lower bound for each forward step ensures acceptable accuracy. Additional constraints on the transition rule are also investigated. The Natural Sciences and Engineering Research Council of Canada (NSERC) and CIENA are acknowledged for financial support.

Spontaneous structural distortion of the metallic Shastry-Sutherland system Dy B4 by quadrupole-spin-lattice coupling

NASA Astrophysics Data System (ADS)

Sim, Hasung; Lee, Seongsu; Hong, Kun-Pyo; Jeong, Jaehong; Zhang, J. R.; Kamiyama, T.; Adroja, D. T.; Murray, C. A.; Thompson, S. P.; Iga, F.; Ji, S.; Khomskii, D.; Park, Je-Geun

2016-11-01

Dy B4 has a two-dimensional Shastry-Sutherland (Sh-S) lattice with strong Ising character of the Dy ions. Despite the intrinsic frustrations, it undergoes two successive transitions: a magnetic ordering at TN=20 K and a quadrupole ordering at TQ=12.5 K . From high-resolution neutron and synchrotron x-ray powder diffraction studies, we have obtained full structural information on this material in all phases and demonstrate that structural modifications occurring at quadrupolar transition lead to the lifting of frustrations inherent in the Sh-S model. Our paper thus provides a complete experimental picture of how the intrinsic frustration of the Sh-S lattice can be lifted by the coupling to quadrupole moments. We show that two other factors, i.e., strong spin-orbit coupling and long-range Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in metallic Dy B4 , play an important role in this behavior.

Field induced phase transition in layered honeycomb spin system α-RuCl3 studied by thermal conductivity

NASA Astrophysics Data System (ADS)

Leahy, Ian; Bornstein, Alex; Choi, Kwang-Yong; Lee, Minhyea

α -RuCl3, a quasi -two-dimensional honeycomb lattice is known to be a candidate material to realize the Heisenberg-Kitaev spin model of a highly anisotropic bond-dependent exchange interaction. We investigate in-plane thermal conductivity (κ) as a function of temperature (T) and in-plane applied field (H). At H = 0 , the onset of a strong increase in κ marks the spontaneous long range ordering temperature, Tc = 6 . 5 K , corresponding to ``zigzag'' antiferromagnetic ordering. A broad peak appearing below Tc in κ was found to be suppressed significantly as H increases up to ~ 7 T , implying the system undergoes a field-induced transition from ordered to a new spin-disordered state analogous to the transverse-field Ising model. Further increasing H above 7 . 1 T , the large field seems to begin polarizing spins thus increasing the phonon mean free path, resulting in a significant rise in κ. This tendency is clearly shown in the field dependence of κ below Tc, which has a pronounced minimum at Hmin = 7 . 1 T . We will discuss our scaling analysis to characterize this field-induced phase transition and compare to the transverse-field Ising spin system. Work at the University of Colorado was supported by the US DOE Basic Energy Sciences under Award No. DE-SC0006888.

Magnetization of the Ising model on the Sierpinski pastry-shell

NASA Astrophysics Data System (ADS)

Chame, Anna; Branco, N. S.

1992-02-01

Using a real-space renormalization group approach, we calculate the approximate magnetization in the Ising model on the Sierpinski Pastry-shell. We consider, as an approximation, only two regions of the fractal: the internal surfaces, or walls (sites on the border of eliminated areas), with coupling constants JS, and the bulk (all other sites), with coupling constants Jv. We obtain the mean magnetization of the two regions as a function of temperature, for different values of α= JS/ JV and different geometric parameters b and l. Curves present a step-like behavior for some values of b and l, as well as different universality classes for the bulk transition.

Phase transitions in coupled map lattices and in associated probabilistic cellular automata.

PubMed

Just, Wolfram

2006-10-01

Analytical tools are applied to investigate piecewise linear coupled map lattices in terms of probabilistic cellular automata. The so-called disorder condition of probabilistic cellular automata is closely related with attracting sets in coupled map lattices. The importance of this condition for the suppression of phase transitions is illustrated by spatially one-dimensional systems. Invariant densities and temporal correlations are calculated explicitly. Ising type phase transitions are found for one-dimensional coupled map lattices acting on repelling sets and for a spatially two-dimensional Miller-Huse-like system with stable long time dynamics. Critical exponents are calculated within a finite size scaling approach. The relevance of detailed balance of the resulting probabilistic cellular automaton for the critical behavior is pointed out.

Out-of-time-ordered correlators in a quantum Ising chain

NASA Astrophysics Data System (ADS)

Lin, Cheng-Ju; Motrunich, Olexei I.

2018-04-01

Out-of-time-ordered correlators (OTOC) have been proposed to characterize quantum chaos in generic systems. However, they can also show interesting behavior in integrable models, resembling the OTOC in chaotic systems in some aspects. Here we study the OTOC for different operators in the exactly-solvable one-dimensional quantum Ising spin chain. The OTOC for spin operators that are local in terms of the Jordan-Wigner fermions has a "shell-like" structure: After the wavefront passes, the OTOC approaches its original value in the long-time limit, showing no signature of scrambling; the approach is described by a t-1 power law at long time t . On the other hand, the OTOC for spin operators that are nonlocal in the Jordan-Wigner fermions has a "ball-like" structure, with its value reaching zero in the long-time limit, looking like a signature of scrambling; the approach to zero, however, is described by a slow power law t-1 /4 for the Ising model at the critical coupling. These long-time power-law behaviors in the lattice model are not captured by conformal field theory calculations. The mixed OTOC with both local and nonlocal operators in the Jordan-Wigner fermions also has a "ball-like" structure, but the limiting values and the decay behavior appear to be nonuniversal. In all cases, we are not able to define a parametrically large window around the wavefront to extract the Lyapunov exponent.

Dynamics of the Random Field Ising Model

NASA Astrophysics Data System (ADS)

Xu, Jian

The Random Field Ising Model (RFIM) is a general tool to study disordered systems. Crackling noise is generated when disordered systems are driven by external forces, spanning a broad range of sizes. Systems with different microscopic structures such as disordered mag- nets and Earth's crust have been studied under the RFIM. In this thesis, we investigated the domain dynamics and critical behavior in two dipole-coupled Ising ferromagnets Nd2Fe14B and LiHoxY 1-xF4. With Tc well above room temperature, Nd2Fe14B has shown reversible disorder when exposed to an external transverse field and crosses between two universality classes in the strong and weak disorder limits. Besides tunable disorder, LiHoxY1-xF4 has shown quantum tunneling effects arising from quantum fluctuations, providing another mechanism for domain reversal. Universality within and beyond power law dependence on avalanche size and energy were studied in LiHo0.65Y0.35 F4.

ISEE 1 charged particle observations indicative of open magnetospheric field lines near the subsolar region

NASA Technical Reports Server (NTRS)

Williams, D. J.; Frank, L. A.

1980-01-01

On November 20, 1977, at 0230-0300 UT, ISEE 1 encountered unusual charged particle distributions within the magnetosphere. The three-dimensional distribution observations for energetic (greater than 24 keV) ions and plasma show the development of field-aligned asymmetries in the energetic ion distributions simultaneously with a marked change in plasma flow. It is concluded that the most likely explanation for these observations is that ISEE 1 encountered open magnetospheric field lines at its position within the magnetosphere (1030 LT and 1200 plus or minus 300 km from the magnetopause). Field lines were open near the geomagnetic equator, and the geometry was spatially or temporally variable. Other features of the field line topology are presented.

Glaubers Ising chain between two thermostats

NASA Astrophysics Data System (ADS)

Cornu, F.; Hilhorst, H. J.

2017-04-01

We consider a one-dimensional Ising model with N spins, each in contact with two thermostats of distinct temperatures, T 1 and T 2. Under Glauber dynamics the stationary state happens to coincide with the equilibrium state at an effective intermediate temperature T≤ft({{T}1},{{T}2}\\right) . The system nevertheless carries a nontrivial energy current between the thermostats. By means of the fermionization technique, for a chain initially in equilibrium at an arbitrary temperature T 0 we calculate the Fourier transform of the probability P≤ft(Q;τ \\right) for the time-integrated energy current Q during a finite time interval τ. In the long time limit we determine the corresponding generating function for the cumulants per site and unit of time, {< {{Q}n}>\\text{c}}/(Nτ ) , and explicitly give those with n  =  1, 2, 3, 4. We exhibit various phenomena in specific regimes: kinetic mean-field effects when one thermostat flips any spin less often than the other one, as well as dissipation towards a thermostat at zero temperature. Moreover, when the system size N goes to infinity while the effective temperature T vanishes, the cumulants of Q per unit of time grow linearly with N and are equal to those of a random walk process. In two adequate scaling regimes involving T and N we exhibit the dependence of the first correction upon the ratio of the spin-spin correlation length ξ (T) and the size N.

Finite-size scaling above the upper critical dimension in Ising models with long-range interactions

NASA Astrophysics Data System (ADS)

Flores-Sola, Emilio J.; Berche, Bertrand; Kenna, Ralph; Weigel, Martin

2015-01-01

The correlation length plays a pivotal role in finite-size scaling and hyperscaling at continuous phase transitions. Below the upper critical dimension, where the correlation length is proportional to the system length, both finite-size scaling and hyperscaling take conventional forms. Above the upper critical dimension these forms break down and a new scaling scenario appears. Here we investigate this scaling behaviour by simulating one-dimensional Ising ferromagnets with long-range interactions. We show that the correlation length scales as a non-trivial power of the linear system size and investigate the scaling forms. For interactions of sufficiently long range, the disparity between the correlation length and the system length can be made arbitrarily large, while maintaining the new scaling scenarios. We also investigate the behavior of the correlation function above the upper critical dimension and the modifications imposed by the new scaling scenario onto the associated Fisher relation.

Trajectory phase transitions and dynamical Lee-Yang zeros of the Glauber-Ising chain.

PubMed

Hickey, James M; Flindt, Christian; Garrahan, Juan P

2013-07-01

We examine the generating function of the time-integrated energy for the one-dimensional Glauber-Ising model. At long times, the generating function takes on a large-deviation form and the associated cumulant generating function has singularities corresponding to continuous trajectory (or "space-time") phase transitions between paramagnetic trajectories and ferromagnetically or antiferromagnetically ordered trajectories. In the thermodynamic limit, the singularities make up a whole curve of critical points in the complex plane of the counting field. We evaluate analytically the generating function by mapping the generator of the biased dynamics to a non-Hermitian Hamiltonian of an associated quantum spin chain. We relate the trajectory phase transitions to the high-order cumulants of the time-integrated energy which we use to extract the dynamical Lee-Yang zeros of the generating function. This approach offers the possibility to detect continuous trajectory phase transitions from the finite-time behavior of measurable quantities.

Thermal conductivity of Ca3Co2O6 single crystals

NASA Astrophysics Data System (ADS)

Che, H. L.; Shi, J.; Wu, J. C.; Rao, X.; Liu, X. G.; Zhao, X.; Sun, X. F.

2018-05-01

Ca3Co2O6 is a rare example of one-dimensional Ising spin-chain material with the moments preferentially aligned along the c axis. In this work, we study the c-axis thermal conductivity (κc) of Ca3Co2O6 single crystal at low temperatures down to 0.3 K and in magnetic fields up to 14 T. The zero-field κc(T) shows a large phonon peak and can be well fitted by using the classical Debye model, which indicates that the heat transport is purely phononic. Moreover, the low-T κc(H) isotherms with H || c display a field-independent behavior. These results indicate that there is no contribution of magnetic excitations to the thermal conductivity in Ca3Co2O6, neither carrying heat nor scattering phonons, which can be attributed to the Ising-like spin anisotropy.

Probing strong correlations with light scattering: Example of the quantum Ising model

DOE PAGES

Babujian, H. M.; Karowski, M.; Tsvelik, A. M.

2016-10-01

In this article we calculate the nonlinear susceptibility and the resonant Raman cross section for the paramagnetic phase of the ferromagnetic quantum Ising model in one dimension. In this region the spectrum of the Ising model has a gap m. The Raman cross section has a strong singularity when the energy of the outgoing photon is at the spectral gap ω f ≈ m and a square root threshold when the frequency difference between the incident and outgoing photons ω i₋ω f≈2m. Finally, the latter feature reflects the fermionic nature of the Ising model excitations.

Probing strong correlations with light scattering: Example of the quantum Ising model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Babujian, H. M.; Karowski, M.; Tsvelik, A. M.

In this article we calculate the nonlinear susceptibility and the resonant Raman cross section for the paramagnetic phase of the ferromagnetic quantum Ising model in one dimension. In this region the spectrum of the Ising model has a gap m. The Raman cross section has a strong singularity when the energy of the outgoing photon is at the spectral gap ω f ≈ m and a square root threshold when the frequency difference between the incident and outgoing photons ω i₋ω f≈2m. Finally, the latter feature reflects the fermionic nature of the Ising model excitations.

Tax Evasion and Nonequilibrium Model on Apollonian Networks

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2012-11-01

The Zaklan model had been proposed and studied recently using the equilibrium Ising model on square lattices (SLs) by [G. Zaklan, F. Westerhoff and D. Stauffer, J. Econ. Interact. Coord.4, 1 (2008), arXiv:0801.2980; G. Zaklan, F. W. S. Lima and F. Westerhoff, Physica A387, 5857 (2008)], near the critical temperature of the Ising model presenting a well-defined phase transition; but on normal and modified Apollonian networks (ANs), [J. S. Andrade, Jr., H. J. Herrmann, R. F. S. Andrade, and L. R. da Silva, Phys. Rev. Lett.94, 018702 (2005); R. F. S. Andrade, J. S. Andrade Jr. and H. J. Herrmann, Phys. Rev. E79, 036105 (2009)] studied the equilibrium Ising model. They showed the equilibrium Ising model not to present on ANs a phase transition of the type for the 2D Ising model. Here, using agent-based Monte Carlo simulations, we study the Zaklan model with the well-known majority-vote model (MVM) with noise and apply it to tax evasion on ANs, to show that differently from the Ising model the MVM on ANs presents a well-defined phase transition. To control the tax evasion in the economics model proposed by Zaklan et al., MVM is applied in the neighborhood of the critical noise qc to the Zaklan model. Here we show that the Zaklan model is robust because this can also be studied, besides using equilibrium dynamics of Ising model, through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.

Thermal contact through a two-temperature kinetic Ising chain

NASA Astrophysics Data System (ADS)

Bauer, M.; Cornu, F.

2018-05-01

We consider a model for thermal contact through a diathermal interface between two macroscopic bodies at different temperatures: an Ising spin chain with nearest neighbor interactions is endowed with a Glauber dynamics with different temperatures and kinetic parameters on alternating sites. The inhomogeneity of the kinetic parameter is a novelty with respect to the model of Racz and Zia (1994 Phys. Rev. E 49 139), and we exhibit its influence upon the stationary non equilibrium values of the two-spin correlations at any distance. By mapping to the dynamics of spin domain walls and using free fermion techniques, we determine the scaled generating function for the cumulants of the exchanged heat amounts per unit of time in the long time limit.

Corruption dynamics model

NASA Astrophysics Data System (ADS)

Malafeyev, O. A.; Nemnyugin, S. A.; Rylow, D.; Kolpak, E. P.; Awasthi, Achal

2017-07-01

The corruption dynamics is analyzed by means of the lattice model which is similar to the three-dimensional Ising model. Agents placed at nodes of the corrupt network periodically choose to perfom or not to perform the act of corruption at gain or loss while making decisions based on the process history. The gain value and its dynamics are defined by means of the Markov stochastic process modelling with parameters established in accordance with the influence of external and individual factors on the agent's gain. The model is formulated algorithmically and is studied by means of the computer simulation. Numerical results are obtained which demonstrate asymptotic behaviour of the corruption network under various conditions.

Fast Rotational Diffusion of Water Molecules in a 2D Hydrogen Bond Network at Cryogenic Temperatures

NASA Astrophysics Data System (ADS)

Prisk, T. R.; Hoffmann, C.; Kolesnikov, A. I.; Mamontov, E.; Podlesnyak, A. A.; Wang, X.; Kent, P. R. C.; Anovitz, L. M.

2018-05-01

Individual water molecules or small clusters of water molecules contained within microporous minerals present an extreme case of confinement where the local structure of hydrogen bond networks are dramatically altered from bulk water. In the zinc silicate hemimorphite, the water molecules form a two-dimensional hydrogen bond network with hydroxyl groups in the crystal framework. Here, we present a combined experimental and theoretical study of the structure and dynamics of water molecules within this network. The water molecules undergo a continuous phase transition in their orientational configuration analogous to a two-dimensional Ising model. The incoherent dynamic structure factor reveals two thermally activated relaxation processes, one on a subpicosecond timescale and another on a 10-100 ps timescale, between 70 and 130 K. The slow process is an in-plane reorientation of the water molecule involving the breaking of hydrogen bonds with a framework that, despite the low temperatures involved, is analogous to rotational diffusion of water molecules in the bulk liquid. The fast process is a localized motion of the water molecule with no apparent analogs among known bulk or confined phases of water.

Fast Rotational Diffusion of Water Molecules in a 2D Hydrogen Bond Network at Cryogenic Temperatures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prisk, Timothy; Hoffmann, Christina; Kolesnikov, Alexander I.

Individual water molecules or small clusters of water molecules contained within microporous minerals present an extreme case of confinement where the local structure of hydrogen bond networks are dramatically altered from bulk water. In the zinc silicate hemimorphite, the water molecules form a two-dimensional hydrogen bond network with hydroxyl groups in the crystal framework. Here in this paper, we present a combined experimental and theoretical study of the structure and dynamics of water molecules within this network. The water molecules undergo a continuous phase transition in their orientational configuration analogous to a two-dimensional Ising model. The incoherent dynamic structure factormore » reveals two thermally activated relaxation processes, one on a subpicosecond timescale and another on a 10–100 ps timescale, between 70 and 130 K. The slow process is an in-plane reorientation of the water molecule involving the breaking of hydrogen bonds with a framework that, despite the low temperatures involved, is analogous to rotational diffusion of water molecules in the bulk liquid. The fast process is a localized motion of the water molecule with no apparent analogs among known bulk or confined phases of water.« less

Fast Rotational Diffusion of Water Molecules in a 2D Hydrogen Bond Network at Cryogenic Temperatures

DOE PAGES

Prisk, Timothy; Hoffmann, Christina; Kolesnikov, Alexander I.; ...

2018-05-09

Individual water molecules or small clusters of water molecules contained within microporous minerals present an extreme case of confinement where the local structure of hydrogen bond networks are dramatically altered from bulk water. In the zinc silicate hemimorphite, the water molecules form a two-dimensional hydrogen bond network with hydroxyl groups in the crystal framework. Here in this paper, we present a combined experimental and theoretical study of the structure and dynamics of water molecules within this network. The water molecules undergo a continuous phase transition in their orientational configuration analogous to a two-dimensional Ising model. The incoherent dynamic structure factormore » reveals two thermally activated relaxation processes, one on a subpicosecond timescale and another on a 10–100 ps timescale, between 70 and 130 K. The slow process is an in-plane reorientation of the water molecule involving the breaking of hydrogen bonds with a framework that, despite the low temperatures involved, is analogous to rotational diffusion of water molecules in the bulk liquid. The fast process is a localized motion of the water molecule with no apparent analogs among known bulk or confined phases of water.« less

Experimental linear-optics simulation of ground-state of an Ising spin chain.

PubMed

Xue, Peng; Zhan, Xian; Bian, Zhihao

2017-05-19

We experimentally demonstrate a photonic quantum simulator: by using a two-spin Ising chain (an isolated dimer) as an example, we encode the wavefunction of the ground state with a pair of entangled photons. The effect of magnetic fields, leading to a critical modification of the correlation between two spins, can be simulated by just local operations. With the ratio of simulated magnetic fields and coupling strength increasing, the ground state of the system changes from a product state to an entangled state and back to another product state. The simulated ground states can be distinguished and the transformations between them can be observed by measuring correlations between photons. This simulation of the Ising model with linear quantum optics opens the door to the future studies which connect quantum information and condensed matter physics.

Toward an Ising Model of Cancer and Beyond

PubMed Central

Torquato, Salvatore

2011-01-01

The holy grail of tumor modeling is to formulate theoretical and computational tools that can be utilized in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth. In order to develop such a predictive model, one must account for the numerous complex mechanisms involved in tumor growth. Here we review resarch work that we have done toward the development of an “Ising model” of cancer. The Ising model is an idealized statistical-mechanical model of ferromagnetism that is based on simple local-interaction rules, but nonetheless leads to basic insights and features of real magnets, such as phase transitions with a critical point. The review begins with a description of a minimalist four-dimensional (three dimensions in space and one in time) cellular automaton (CA) model of cancer in which healthy cells transition between states (proliferative, hypoxic, and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to model the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment, including induced resistance, is then described. How angiogenesis as well as the heterogeneous and confined environment in which a tumor grows is incorporated in the CA model is discussed. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently described. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility, oncogenes, tumor suppressor genes and cell-cell communication. A discussion about the need to bring to bear the powerful machinery of the theory of heterogeneous media to better understand the behavior of cancer in its microenvironment is presented. Finally, we propose the possibility of using optimization techniques, which have been used profitably to understand physical phenomena, in order to devise therapeutic (chemotherapy/radiation) strategies and to understand tumorigenesis itself. PMID:21301063

Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction

NASA Astrophysics Data System (ADS)

Chan, Yang-Hao; Jin, Wen; Jiang, Hong-Chen; Starykh, Oleg A.

2017-12-01

We report a combined analytical and density matrix renormalized group study of the antiferromagnetic X X Z spin-1 /2 Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya (DM) interaction and a transverse magnetic field. The numerically determined phase diagram of this model, which features two ordered Ising phases and a critical Luttinger liquid, one with fully broken spin-rotational symmetry, agrees well with the predictions of Garate and Affleck [I. Garate and I. Affleck, Phys. Rev. B 81, 144419 (2010), 10.1103/PhysRevB.81.144419]. We also confirm the prevalence of the Nz Néel Ising order in the regime of comparable DM and magnetic field magnitudes.

Unusual specific heat of almost dry L-cysteine and L-cystine amino acids.

PubMed

Ishikawa, M S; Lima, T A; Ferreira, F F; Martinho, H S

2015-03-01

A detailed quantitative analysis of the specific heat in the 0.5- to 200-K temperature range for almost dry L-cysteine and its dimer, L-cystine, amino acids is presented. We report the occurrence of a sharp first-order transition at ∼76 K for L-cysteine associated with the thiol group ordering which was successfully modeled with the two-dimensional Ising model. We demonstrated that quantum rotors, two-level systems (TLS), Einstein oscillators, and acoustic phonons (the Debye model) are essential ingredients to correctly describe the overall experimental data. Our analysis pointed out the absence of the TLS contribution to the low temperature specific heat of L-cysteine. This result was similar to that found in other noncrystalline amorphous materials, e.g., amorphous silicon, low density amorphous water, and ultrastable glasses. L-cystine presented an unusual nonlinear acoustic dispersion relation ω(q)=vq0.95 and a Maxwell-Boltzmann-type distribution of tunneling barriers. The presence of Einstein oscillators with ΘE∼70 K was common in both systems and adequately modeled the boson peak contributions.

Physics-based statistical learning approach to mesoscopic model selection.

PubMed

Taverniers, Søren; Haut, Terry S; Barros, Kipton; Alexander, Francis J; Lookman, Turab

2015-11-01

In materials science and many other research areas, models are frequently inferred without considering their generalization to unseen data. We apply statistical learning using cross-validation to obtain an optimally predictive coarse-grained description of a two-dimensional kinetic nearest-neighbor Ising model with Glauber dynamics (GD) based on the stochastic Ginzburg-Landau equation (sGLE). The latter is learned from GD "training" data using a log-likelihood analysis, and its predictive ability for various complexities of the model is tested on GD "test" data independent of the data used to train the model on. Using two different error metrics, we perform a detailed analysis of the error between magnetization time trajectories simulated using the learned sGLE coarse-grained description and those obtained using the GD model. We show that both for equilibrium and out-of-equilibrium GD training trajectories, the standard phenomenological description using a quartic free energy does not always yield the most predictive coarse-grained model. Moreover, increasing the amount of training data can shift the optimal model complexity to higher values. Our results are promising in that they pave the way for the use of statistical learning as a general tool for materials modeling and discovery.

Many-body localization in Ising models with random long-range interactions

NASA Astrophysics Data System (ADS)

Li, Haoyuan; Wang, Jia; Liu, Xia-Ji; Hu, Hui

2016-12-01

We theoretically investigate the many-body localization phase transition in a one-dimensional Ising spin chain with random long-range spin-spin interactions, Vi j∝|i-j |-α , where the exponent of the interaction range α can be tuned from zero to infinitely large. By using exact diagonalization, we calculate the half-chain entanglement entropy and the energy spectral statistics and use them to characterize the phase transition towards the many-body localization phase at infinite temperature and at sufficiently large disorder strength. We perform finite-size scaling to extract the critical disorder strength and the critical exponent of the divergent localization length. With increasing α , the critical exponent experiences a sharp increase at about αc≃1.2 and then gradually decreases to a value found earlier in a disordered short-ranged interacting spin chain. For α <αc , we find that the system is mostly localized and the increase in the disorder strength may drive a transition between two many-body localized phases. In contrast, for α >αc , the transition is from a thermalized phase to the many-body localization phase. Our predictions could be experimentally tested with an ion-trap quantum emulator with programmable random long-range interactions, or with randomly distributed Rydberg atoms or polar molecules in lattices.

Ultrathin nanosheets of CrSiTe 3. A semiconducting two-dimensional ferromagnetic material

DOE PAGES

Lin, Ming -Wei; Zhung, Houlong L.; Yan, Jiaqiang; ...

2015-11-27

Finite range ferromagnetism and antiferromagnetism in two-dimensional (2D) systems within an isotropic Heisenberg model at non-zero temperature were originally proposed to be impossible. However, recent theoretical studies using an Ising model have recently shown that 2D magnetic crystals can exhibit magnetism. Experimental verification of existing 2D magnetic crystals in this system has remained elusive. In this work we for the first time exfoliate the CrSiTe 3, a bulk ferromagnetic semiconductor, to mono- and few-layer 2D crystals onto a Si/SiO 2 substrate. The Raman spectra show the good stability and high quality of the exfoliated flakes, consistent with the computed phononmore » spectra of 2D CrSiTe 3, giving a strong evidence for the existence of 2D CrSiTe 3 crystals. When the thickness of the CrSiTe 3 crystals is reduced to few-layers, we observed a clear change in resistivity at 80~120 K, consistent with the theoretical calculations on the Curie temperature (Tc) of ~80 K for the magnetic ordering of 2D CrSiTe 3 crystals. As a result, the ferromagnetic mono- and few-layer 2D CrSiTe 3 indicated here should enable numerous applications in nano-spintronics.« less

One Dimensional(1D)-to-2D Crossover of Spin Correlations in the 3D Magnet ZnMn 2O 4

DOE PAGES

Disseler, S. M.; Chen, Y.; Yeo, S.; ...

2015-12-08

In this paper we report on the intriguing evolution of the dynamical spin correlations of the frustrated spinel ZnMn 2O 4. Inelastic neutron scattering and magnetization studies reveal that the dynamical correlations at high temperatures are 1D. At lower temperature, these dynamical correlations become 2D. Surprisingly, the dynamical correlations condense into a quasi 2D Ising-like ordered state, making this a rare observation of two dimensional order on the spinel lattice. Remarkably, 3D ordering is not observed down to temperatures as low as 300 mK. This unprecedented dimensional crossover stems from frustrated exchange couplings due to the huge Jahn-Teller distortions aroundmore » Mn 3+ ions on the spinel lattice.« less

From near to eternity: Spin-glass planting, tiling puzzles, and constraint-satisfaction problems

NASA Astrophysics Data System (ADS)

Hamze, Firas; Jacob, Darryl C.; Ochoa, Andrew J.; Perera, Dilina; Wang, Wenlong; Katzgraber, Helmut G.

2018-04-01

We present a methodology for generating Ising Hamiltonians of tunable complexity and with a priori known ground states based on a decomposition of the model graph into edge-disjoint subgraphs. The idea is illustrated with a spin-glass model defined on a cubic lattice, where subproblems, whose couplers are restricted to the two values {-1 ,+1 } , are specified on unit cubes and are parametrized by their local degeneracy. The construction is shown to be equivalent to a type of three-dimensional constraint-satisfaction problem known as the tiling puzzle. By varying the proportions of subproblem types, the Hamiltonian can span a dramatic range of typical computational complexity, from fairly easy to many orders of magnitude more difficult than prototypical bimodal and Gaussian spin glasses in three space dimensions. We corroborate this behavior via experiments with different algorithms and discuss generalizations and extensions to different types of graphs.

Renormalization of concurrence: The application of the quantum renormalization group to quantum-information systems

NASA Astrophysics Data System (ADS)

Kargarian, M.; Jafari, R.; Langari, A.

2007-12-01

We have combined the idea of renormalization group and quantum-information theory. We have shown how the entanglement or concurrence evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. Moreover, we introduce how the renormalization-group approach can be implemented to obtain the quantum-information properties of a many-body system. We have obtained the concurrence as a measure of entanglement, its derivatives and their scaling behavior versus the size of system for the one-dimensional Ising model in transverse field. We have found that the derivative of concurrence between two blocks each containing half of the system size diverges at the critical point with the exponent, which is directly associated with the divergence of the correlation length.

Quantum simulation of transverse Ising models with Rydberg atoms

NASA Astrophysics Data System (ADS)

Schauss, Peter

2018-04-01

Quantum Ising models are canonical models for the study of quantum phase transitions (Sachdev 1999 Quantum Phase Transitions (Cambridge: Cambridge University Press)) and are the underlying concept for many analogue quantum computing and quantum annealing ideas (Tanaka et al Quantum Spin Glasses, Annealing and Computation (Cambridge: Cambridge University Press)). Here we focus on the implementation of finite-range interacting Ising spin models, which are barely tractable numerically. Recent experiments with cold atoms have reached the interaction-dominated regime in quantum Ising magnets via optical coupling of trapped neutral atoms to Rydberg states. This approach allows for the tunability of all relevant terms in an Ising spin Hamiltonian with 1/{r}6 interactions in transverse and longitudinal fields. This review summarizes the recent progress of these implementations in Rydberg lattices with site-resolved detection. Strong correlations in quantum Ising models have been observed in several experiments, starting from a single excitation in the superatom regime up to the point of crystallization. The rapid progress in this field makes spin systems based on Rydberg atoms a promising platform for quantum simulation because of the unmatched flexibility and strength of interactions combined with high control and good isolation from the environment.

Diffusion on an Ising chain with kinks

NASA Astrophysics Data System (ADS)

Hamma, Alioscia; Mansour, Toufik; Severini, Simone

2009-07-01

We count the number of histories between the two degenerate minimum energy configurations of the Ising model on a chain, as a function of the length n and the number d of kinks that appear above the critical temperature. This is equivalent to count permutations of length n avoiding certain subsequences depending on d. We give explicit generating functions and compute the asymptotics. The setting considered has a role when describing dynamics induced by quantum Hamiltonians with deconfined quasi-particles.

Stochastic thermodynamics for Ising chain and symmetric exclusion process.

PubMed

Toral, R; Van den Broeck, C; Escaff, D; Lindenberg, Katja

2017-03-01

We verify the finite-time fluctuation theorem for a linear Ising chain in contact with heat reservoirs at its ends. Analytic results are derived for a chain consisting of two spins. The system can be mapped onto a model for particle transport, namely, the symmetric exclusion process in contact with thermal and particle reservoirs. We modify the symmetric exclusion process to represent a thermal engine and reproduce universal features of the efficiency at maximum power.

Evolutionary games with self-questioning adaptive mechanism and the Ising model

NASA Astrophysics Data System (ADS)

Liu, J.; Xu, C.; Hui, P. M.

2017-09-01

A class of evolutionary games using a self-questioning strategy switching mechanism played in a population of connected agents is shown to behave as an Ising model Hamiltonian of spins connected in the same way. The payoff parameters combine to give the coupling between spins and an external magnetic field. The mapping covers the prisoner's dilemma, snowdrift and stag hunt games in structured populations. A well-mixed system is used to illustrate the equivalence. In a chain of agents/spins, the mapping to Ising model leads to an exact solution to the games effortlessly. The accuracy of standard approximations on the games can then be quantified. The site approximation is found to show varied accuracies depending on the payoff parameters, and the link approximation is shown to give the exact result in a chain but not in a closed form. The mapping established here connects two research areas, with each having much to offer to the other.

Correction of defective pixels for medical and space imagers based on Ising Theory

NASA Astrophysics Data System (ADS)

Cohen, Eliahu; Shnitser, Moriel; Avraham, Tsvika; Hadar, Ofer

2014-09-01

We propose novel models for image restoration based on statistical physics. We investigate the affinity between these fields and describe a framework from which interesting denoising algorithms can be derived: Ising-like models and simulated annealing techniques. When combined with known predictors such as Median and LOCO-I, these models become even more effective. In order to further examine the proposed models we apply them to two important problems: (i) Digital Cameras in space damaged from cosmic radiation. (ii) Ultrasonic medical devices damaged from speckle noise. The results, as well as benchmark and comparisons, suggest in most of the cases a significant gain in PSNR and SSIM in comparison to other filters.

Hyperscaling breakdown and Ising spin glasses: The Binder cumulant

NASA Astrophysics Data System (ADS)

Lundow, P. H.; Campbell, I. A.

2018-02-01

Among the Renormalization Group Theory scaling rules relating critical exponents, there are hyperscaling rules involving the dimension of the system. It is well known that in Ising models hyperscaling breaks down above the upper critical dimension. It was shown by Schwartz (1991) that the standard Josephson hyperscaling rule can also break down in Ising systems with quenched random interactions. A related Renormalization Group Theory hyperscaling rule links the critical exponents for the normalized Binder cumulant and the correlation length in the thermodynamic limit. An appropriate scaling approach for analyzing measurements from criticality to infinite temperature is first outlined. Numerical data on the scaling of the normalized correlation length and the normalized Binder cumulant are shown for the canonical Ising ferromagnet model in dimension three where hyperscaling holds, for the Ising ferromagnet in dimension five (so above the upper critical dimension) where hyperscaling breaks down, and then for Ising spin glass models in dimension three where the quenched interactions are random. For the Ising spin glasses there is a breakdown of the normalized Binder cumulant hyperscaling relation in the thermodynamic limit regime, with a return to size independent Binder cumulant values in the finite-size scaling regime around the critical region.

A thermodynamic counterpart of the Axelrod model of social influence: The one-dimensional case

NASA Astrophysics Data System (ADS)

Gandica, Y.; Medina, E.; Bonalde, I.

2013-12-01

We propose a thermodynamic version of the Axelrod model of social influence. In one-dimensional (1D) lattices, the thermodynamic model becomes a coupled Potts model with a bonding interaction that increases with the site matching traits. We analytically calculate thermodynamic and critical properties for a 1D system and show that an order-disorder phase transition only occurs at T=0 independent of the number of cultural traits q and features F. The 1D thermodynamic Axelrod model belongs to the same universality class of the Ising and Potts models, notwithstanding the increase of the internal dimension of the local degree of freedom and the state-dependent bonding interaction. We suggest a unifying proposal to compare exponents across different discrete 1D models. The comparison with our Hamiltonian description reveals that in the thermodynamic limit the original out-of-equilibrium 1D Axelrod model with noise behaves like an ordinary thermodynamic 1D interacting particle system.

Nonequilibrium dynamic critical scaling of the quantum Ising chain.

PubMed

Kolodrubetz, Michael; Clark, Bryan K; Huse, David A

2012-07-06

We solve for the time-dependent finite-size scaling functions of the one-dimensional transverse-field Ising chain during a linear-in-time ramp of the field through the quantum critical point. We then simulate Mott-insulating bosons in a tilted potential, an experimentally studied system in the same equilibrium universality class, and demonstrate that universality holds for the dynamics as well. We find qualitatively athermal features of the scaling functions, such as negative spin correlations, and we show that they should be robustly observable within present cold atom experiments.

Data compressor designed to improve recognition of magnetic phases

NASA Astrophysics Data System (ADS)

Vogel, E. E.; Saravia, G.; Cortez, L. V.

2012-02-01

Data compressors available in the web have been used to determine magnetic phases for two-dimensional (2D) systems [E. Vogel, G. Saravia, F. Bachmann, B. Fierro, J. Fischer, Phase transitions in Edwards-Anderson model by means of information theory, Physica A 388 2009 4075-4082]. In the present work, we push this line forward along four different directions. First, the compressor itself: we design a new data compressor, named wlzip, optimized for the recognition of information having physical (or scientific) information instead of the random digital information usually compressed. Second, for the first time we extend the data compression analysis to the 3D Ising ferromagnetic model using wlzip. Third, we discuss the tuning possibilities of wlzip in terms of the number of digits considered in the compression to yield maximum definition; in this way, the transition temperature of both 2D and 3D Ising ferromagnets can be reported with very good resolution. Fourth, the extension of the time window through which the data file is actually compressed is also considered to get optimum accuracy. The paper is focused on the new compressor, its algorithm in general and the way to apply it. Advantages and disadvantages of wlzip are discussed. Toward the end, we mention other possible applications of this technique to recognize stable and unstable regimes in the evolution of variables in meteorology (such as pollution content or atmospheric pressure), biology (blood pressure) and econophysics (prices of the stock market).

Long-time predictability in disordered spin systems following a deep quench

NASA Astrophysics Data System (ADS)

Ye, J.; Gheissari, R.; Machta, J.; Newman, C. M.; Stein, D. L.

2017-04-01

We study the problem of predictability, or "nature vs nurture," in several disordered Ising spin systems evolving at zero temperature from a random initial state: How much does the final state depend on the information contained in the initial state, and how much depends on the detailed history of the system? Our numerical studies of the "dynamical order parameter" in Edwards-Anderson Ising spin glasses and random ferromagnets indicate that the influence of the initial state decays as dimension increases. Similarly, this same order parameter for the Sherrington-Kirkpatrick infinite-range spin glass indicates that this information decays as the number of spins increases. Based on these results, we conjecture that the influence of the initial state on the final state decays to zero in finite-dimensional random-bond spin systems as dimension goes to infinity, regardless of the presence of frustration. We also study the rate at which spins "freeze out" to a final state as a function of dimensionality and number of spins; here the results indicate that the number of "active" spins at long times increases with dimension (for short-range systems) or number of spins (for infinite-range systems). We provide theoretical arguments to support these conjectures, and also study analytically several mean-field models: the random energy model, the uniform Curie-Weiss ferromagnet, and the disordered Curie-Weiss ferromagnet. We find that for these models, the information contained in the initial state does not decay in the thermodynamic limit—in fact, it fully determines the final state. Unlike in short-range models, the presence of frustration in mean-field models dramatically alters the dynamical behavior with respect to the issue of predictability.

Long-time predictability in disordered spin systems following a deep quench.

PubMed

Ye, J; Gheissari, R; Machta, J; Newman, C M; Stein, D L

2017-04-01

We study the problem of predictability, or "nature vs nurture," in several disordered Ising spin systems evolving at zero temperature from a random initial state: How much does the final state depend on the information contained in the initial state, and how much depends on the detailed history of the system? Our numerical studies of the "dynamical order parameter" in Edwards-Anderson Ising spin glasses and random ferromagnets indicate that the influence of the initial state decays as dimension increases. Similarly, this same order parameter for the Sherrington-Kirkpatrick infinite-range spin glass indicates that this information decays as the number of spins increases. Based on these results, we conjecture that the influence of the initial state on the final state decays to zero in finite-dimensional random-bond spin systems as dimension goes to infinity, regardless of the presence of frustration. We also study the rate at which spins "freeze out" to a final state as a function of dimensionality and number of spins; here the results indicate that the number of "active" spins at long times increases with dimension (for short-range systems) or number of spins (for infinite-range systems). We provide theoretical arguments to support these conjectures, and also study analytically several mean-field models: the random energy model, the uniform Curie-Weiss ferromagnet, and the disordered Curie-Weiss ferromagnet. We find that for these models, the information contained in the initial state does not decay in the thermodynamic limit-in fact, it fully determines the final state. Unlike in short-range models, the presence of frustration in mean-field models dramatically alters the dynamical behavior with respect to the issue of predictability.

On the number of infinite geodesics and ground states in disordered systems

NASA Astrophysics Data System (ADS)

Wehr, Jan

1997-04-01

We study first-passage percolation models and their higher dimensional analogs—models of surfaces with random weights. We prove that under very general conditions the number of lines or, in the second case, hypersurfaces which locally minimize the sum of the random weights is with probability one equal to 0 or with probability one equal to +∞. As corollaries we show that in any dimension d≥2 the number of ground states of an Ising ferromagnet with random coupling constants equals (with probability one) 2 or +∞. Proofs employ simple large-deviation estimates and ergodic arguments.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukherjee, Swagato; Venugopalan, Raju; Yin, Yi

Exploiting the universality between the QCD critical point and the three-dimensional Ising model, closed form expressions derived for nonequilibrium critical cumulants on the crossover side of the critical point reveal that they can differ in both magnitude and sign from equilibrium expectations. Here, we demonstrate here that key elements of the Kibble-Zurek framework of nonequilibrium phase transitions can be employed to describe the dynamics of these critical cumulants. Lastly, our results suggest that observables sensitive to critical dynamics in heavy-ion collisions should be expressible as universal scaling functions, thereby providing powerful model-independent guidance in searches for the QCD critical point.

Quasi-phases and pseudo-transitions in one-dimensional models with nearest neighbor interactions

NASA Astrophysics Data System (ADS)

de Souza, S. M.; Rojas, Onofre

2018-01-01

There are some particular one-dimensional models, such as the Ising-Heisenberg spin models with a variety of chain structures, which exhibit unexpected behaviors quite similar to the first and second order phase transition, which could be confused naively with an authentic phase transition. Through the analysis of the first derivative of free energy, such as entropy, magnetization, and internal energy, a "sudden" jump that closely resembles a first-order phase transition at finite temperature occurs. However, by analyzing the second derivative of free energy, such as specific heat and magnetic susceptibility at finite temperature, it behaves quite similarly to a second-order phase transition exhibiting an astonishingly sharp and fine peak. The correlation length also confirms the evidence of this pseudo-transition temperature, where a sharp peak occurs at the pseudo-critical temperature. We also present the necessary conditions for the emergence of these quasi-phases and pseudo-transitions.

Critical frontier of the triangular Ising antiferromagnet in a field

NASA Astrophysics Data System (ADS)

Qian, Xiaofeng; Wegewijs, Maarten; Blöte, Henk W.

2004-03-01

We study the critical line of the triangular Ising antiferromagnet in an external magnetic field by means of a finite-size analysis of results obtained by transfer-matrix and Monte Carlo techniques. We compare the shape of the critical line with predictions of two different theoretical scenarios. Both scenarios, while plausible, involve assumptions. The first scenario is based on the generalization of the model to a vertex model, and the assumption that the exact analytic form of the critical manifold of this vertex model is determined by the zeroes of an O(2) gauge-invariant polynomial in the vertex weights. However, it is not possible to fit the coefficients of such polynomials of orders up to 10, such as to reproduce the numerical data for the critical points. The second theoretical prediction is based on the assumption that a renormalization mapping exists of the Ising model on the Coulomb gas, and analysis of the resulting renormalization equations. It leads to a shape of the critical line that is inconsistent with the first prediction, but consistent with the numerical data.

The Ising model coupled to 2d orders

NASA Astrophysics Data System (ADS)

Glaser, Lisa

2018-04-01

In this article we make first steps in coupling matter to causal set theory in the path integral. We explore the case of the Ising model coupled to the 2d discrete Einstein Hilbert action, restricted to the 2d orders. We probe the phase diagram in terms of the Wick rotation parameter β and the Ising coupling j and find that the matter and the causal sets together give rise to an interesting phase structure. The couplings give rise to five different phases. The causal sets take on random or crystalline characteristics as described in Surya (2012 Class. Quantum Grav. 29 132001) and the Ising model can be correlated or uncorrelated on the random orders and correlated, uncorrelated or anti-correlated on the crystalline orders. We find that at least one new phase transition arises, in which the Ising spins push the causal set into the crystalline phase.

The acceleration of charged particles in interplanetary shock waves

NASA Technical Reports Server (NTRS)

Pesses, M. E.; Decker, R. B.; Armstrong, T. P.

1982-01-01

Consideration of the theoretical and observational literature on energetic ion acceleration in interplanetary shock waves is the basis for the present discussion of the shock acceleration of the solar wind plasma and particle transport effects. It is suggested that ISEE data be used to construct data sets for shock events that extend continuously from solar wind to galactic cosmic ray energies, including data for electrons, protons, alphas and ions with Z values greater than 2.0, and that the temporal and spatial evolution of two- and three-dimensional particle distribution functions be studied by means of two or more spacecraft.

Strong-coupling analysis of two-dimensional O({ital N}) {sigma} models with {ital N}{le}2 on square, triangular, and honeycomb lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campostrini, M.; Pelissetto, A.; Rossi, P.

1996-09-01

The critical behavior of two-dimensional (2D) O({ital N}) {sigma} models with {ital N}{le}2 on square, triangular, and honeycomb lattices is investigated by an analysis of the strong-coupling expansion of the two-point fundamental Green{close_quote}s function {ital G}({ital x}), calculated up to 21st order on the square lattice, 15th order on the triangular lattice, and 30th order on the honeycomb lattice. For {ital N}{lt}2 the critical behavior is of power-law type, and the exponents {gamma} and {nu} extracted from our strong-coupling analysis confirm exact results derived assuming universality with solvable solid-on-solid models. At {ital N}=2, i.e., for the 2D {ital XY} model,more » the results from all lattices considered are consistent with the Kosterlitz-Thouless exponential approach to criticality, characterized by an exponent {sigma}=1/2, and with universality. The value {sigma}=1/2 is confirmed within an uncertainty of few percent. The prediction {eta}=1/4 is also roughly verified. For various values of {ital N}{le}2, we determine some ratios of amplitudes concerning the two-point function {ital G}({ital x}) in the critical limit of the symmetric phase. This analysis shows that the low-momentum behavior of {ital G}({ital x}) in the critical region is essentially Gaussian at all values of {ital N}{le}2. Exact results for the long-distance behavior of {ital G}({ital x}) when {ital N}=1 (Ising model in the strong-coupling phase) confirm this statement. {copyright} {ital 1996 The American Physical Society.}« less

Effective potential of the three-dimensional Ising model: The pseudo-ɛ expansion study

NASA Astrophysics Data System (ADS)

Sokolov, A. I.; Kudlis, A.; Nikitina, M. A.

2017-08-01

The ratios R2k of renormalized coupling constants g2k that enter the effective potential and small-field equation of state acquire the universal values at criticality. They are calculated for the three-dimensional scalar λϕ4 field theory (3D Ising model) within the pseudo-ɛ expansion approach. Pseudo-ɛ expansions for the critical values of g6, g8, g10, R6 =g6 / g42, R8 =g8 / g43 and R10 =g10 / g44 originating from the five-loop renormalization group (RG) series are derived. Pseudo-ɛ expansions for the sextic coupling have rapidly diminishing coefficients, so addressing Padé approximants yields proper numerical results. Use of Padé-Borel-Leroy and conformal mapping resummation techniques further improves the accuracy leading to the values R6* = 1.6488 and R6* = 1.6490 which are in a brilliant agreement with the result of advanced lattice calculations. For the octic coupling the numerical structure of the pseudo-ɛ expansions is less favorable. Nevertheless, the conform-Borel resummation gives R8* = 0.868, the number being close to the lattice estimate R8* = 0.871 and compatible with the result of 3D RG analysis R8* = 0.857. Pseudo-ɛ expansions for R10* and g10* are also found to have much smaller coefficients than those of the original RG series. They remain, however, fast growing and big enough to prevent obtaining fair numerical estimates.

Magnetopause modeling - Flux transfer events and magnetosheath quasi-trapped distributions

NASA Technical Reports Server (NTRS)

Speiser, T. W.; Williams, D. J.

1982-01-01

Three-dimensional distribution functions for energetic ions are studied numerically in the magnetosphere, through the magnetopause, and in the magnetosheath using a simple one-dimensional quasi-static model and ISEE 1 magnetopause crossing data for November 10, 1977. Quasi-trapped populations in the magnetosheath observed near flux transfer events (FTEs) are investigated, and it is shown that the population in the sheath appears to sandwich the FTE distributions. These quasi-trapped distributions are due to slow, large pitch angle, outward moving particles left behind by the outward rush of the ions more field-aligned at the time the flux was opened. It is found that sheath convective flows can map along the connected flux tube without drastically changing the distribution function, and results suggest that localized tangential fields above the upper limit may exist.

Environment overwhelms both nature and nurture in a model spin glass

NASA Astrophysics Data System (ADS)

Middleton, A. Alan; Yang, Jie

We are interested in exploring what information determines the particular history of the glassy long term dynamics in a disordered material. We study the effect of initial configurations and the realization of stochastic dynamics on the long time evolution of configurations in a two-dimensional Ising spin glass model. The evolution of nearest neighbor correlations is computed using patchwork dynamics, a coarse-grained numerical heuristic for temporal evolution. The dependence of the nearest neighbor spin correlations at long time on both initial spin configurations and noise histories are studied through cross-correlations of long-time configurations and the spin correlations are found to be independent of both. We investigate how effectively rigid bond clusters coarsen. Scaling laws are used to study the convergence of configurations and the distribution of sizes of nearly rigid clusters. The implications of the computational results on simulations and phenomenological models of spin glasses are discussed. We acknowledge NSF support under DMR-1410937 (CMMT program).

Two-dimensional lattice gauge theories with superconducting quantum circuits

PubMed Central

Marcos, D.; Widmer, P.; Rico, E.; Hafezi, M.; Rabl, P.; Wiese, U.-J.; Zoller, P.

2014-01-01

A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability. PMID:25512676

Ordering of two-dimensional crystals confined in strips of finite width

NASA Astrophysics Data System (ADS)

Ricci, A.; Nielaba, P.; Sengupta, S.; Binder, K.

2007-01-01

Monte Carlo simulations are used to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential ∝r-12 in d=2 dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width D ) depends very sensitively on the precise boundary conditions at the two “walls” providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and such surface-induced order persists near the boundaries also at temperatures where the system in the bulk is in its fluid state. However, using smooth repulsive boundaries as walls providing the confinement, only the orientational order is enhanced, but positional (quasi-)long range order is destroyed: The mean-square displacement of two particles n lattice parameters apart in the y direction along the walls then crosses over from the logarithmic increase (characteristic for d=2 ) to a linear increase with n (characteristic for d=1 ). The strip then exhibits a vanishing shear modulus. These results are interpreted in terms of a phenomenological harmonic theory. Also the effect of incommensurability of the strip width D with the triangular lattice structure is discussed, and a comparison with surface effects on phase transitions in simple Ising and XY models is made.

On a three-dimensional symmetric Ising tetrahedron and contributions to the theory of the dilogarithm and Clausen functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coffey, Mark W.

2008-04-15

Perturbative quantum field theory for the Ising model at the three-loop level yields a tetrahedral Feynman diagram C(a,b) with masses a and b and four other lines with unit mass. The completely symmetric tetrahedron C{sup Tet}{identical_to}C(1,1) has been of interest from many points of view, with several representations and conjectures having been given in the literature. We prove a conjectured exponentially fast convergent sum for C(1,1), as well as a previously empirical relation for C(1,1) as a remarkable difference of Clausen function values. Our presentation includes propositions extending the theory of the dilogarithm Li{sub 2} and Clausen Cl{sub 2} functions,more » as well as their relation to other special functions of mathematical physics. The results strengthen connections between Feynman diagram integrals, volumes in hyperbolic space, number theory, and special functions and numbers, specifically including dilogarithms, Clausen function values, and harmonic numbers.« less

Fluctuation in the Intermediate Magnetic Phase of Triangular Ising Antiferromagnet (CeS)1.16[Fe0.33(NbS2)2

NASA Astrophysics Data System (ADS)

Michioka, Chishiro; Suzuki, Kazuya; Mibu, Ko

2002-10-01

We applied 57Fe Mössbauer spectroscopy for investigating the Ising spin triangular lattice antiferromagnet (TLA) (CeS)1.16[Fe0.33(NbS2)2] between 2 and 300 K. The spectra revealed that the relaxation time of the hyperfine field markedly changes in the intermediate phase between TN1=22 K and TN2=15 K due to strong spin fluctuation. The relaxation of the hyperfine field is not sufficiently fast as a paramagnet even at 77 K, which is much higher than TN1, and the inverse susceptibility of (LaS)1.14[Fe0.33(NbS2)2] deviates from the Curie-Weiss law below 100 K. These results indicate that an unusual short-range order exists above TN1. The temperature dependence of the Mössbauer spectra can be explained by phase transition of the three-dimensional TLA model with weak interlayer exchange interactions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Basu, Banasri; Bandyopadhyay, Pratul; Majumdar, Priyadarshi

We have studied quantum phase transition induced by a quench in different one-dimensional spin systems. Our analysis is based on the dynamical mechanism which envisages nonadiabaticity in the vicinity of the critical point. This causes spin fluctuation which leads to the random fluctuation of the Berry phase factor acquired by a spin state when the ground state of the system evolves in a closed path. The two-point correlation of this phase factor is associated with the probability of the formation of defects. In this framework, we have estimated the density of defects produced in several one-dimensional spin chains. At themore » critical region, the entanglement entropy of a block of L spins with the rest of the system is also estimated which is found to increase logarithmically with L. The dependence on the quench time puts a constraint on the block size L. It is also pointed out that the Lipkin-Meshkov-Glick model in point-splitting regularized form appears as a combination of the XXX model and Ising model with magnetic field in the negative z axis. This unveils the underlying conformal symmetry at criticality which is lost in the sharp point limit. Our analysis shows that the density of defects as well as the scaling behavior of the entanglement entropy follows a universal behavior in all these systems.« less

Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure

NASA Astrophysics Data System (ADS)

Mong, Roger S. K.; Clarke, David J.; Alicea, Jason; Lindner, Netanel H.; Fendley, Paul; Nayak, Chetan; Oreg, Yuval; Stern, Ady; Berg, Erez; Shtengel, Kirill; Fisher, Matthew P. A.

2014-01-01

Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here, we establish a similar correspondence between the Z3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that—unlike Ising anyons—allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane's construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a twofold ground-state degeneracy on a torus. In contrast to a p+ip superconductor, vortices do not yield additional particle types, yet depending on nonuniversal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements.

Magnetic Correlations in the Triangular Antiferromagnet TbInO3

NASA Astrophysics Data System (ADS)

Sala, Gabriele; Clark, Lucy; Maharaj, Dalini; Stone, Matthew B.; Knight, Kevin S.; Cheong, Sang-Wook; Gaulin, Bruce D.

TbInO3 crystallizes with a hexagonal P63 cm structure in which layers of edge-sharing triangles of magnetic Tb3+ ions are separated by non-magnetic [InO5]7- units. TbInO3, therefore, realizes an excellent opportunity to explore the behavior of a two-dimensional magnetic triangular lattice, a canonical model of geometric frustration. Here we present our study of a polycrystalline sample of TbInO3. Our high resolution powder neutron diffraction data (HRPD, ISIS) of TbInO3 confirm that the triangular layers of Tb3+ remain undistorted to at least 0 . 46 K. Magnetic susceptibility data follow Curie-Weiss behavior over a wide range of T with θ = - 17 . 19 (3) K indicating the dominance of antiferromagnetic correlations. The susceptibility data also show an absence of conventional long-range spin order down to at least 0 . 55 K, reflecting the frustrated nature of TbInO3. Elastic magnetic diffuse neutron scattering (SEQUOIA, SNS) is observed below ~ 15 K, due to the presence of static two-dimensional spin correlations. The spectrum of crystal field excitations in TbInO3 appears to have an exotic form due to the existence of two crystallographically distinct Tb3+ sites and leads to a strong Ising anisotropy of the spin symmetry.

Entanglement of two blocks of spins in the critical Ising model

NASA Astrophysics Data System (ADS)

Facchi, P.; Florio, G.; Invernizzi, C.; Pascazio, S.

2008-11-01

We compute the entropy of entanglement of two blocks of L spins at a distance d in the ground state of an Ising chain in an external transverse magnetic field. We numerically study the von Neumann entropy for different values of the transverse field. At the critical point we obtain analytical results for blocks of size L=1 and 2. In the general case, the critical entropy is shown to be additive when d→∞ . Finally, based on simple arguments, we derive an expression for the entropy at the critical point as a function of both L and d . This formula is in excellent agreement with numerical results.

Average configuration of the distant (less than 220-earth-radii) magnetotail - Initial ISEE-3 magnetic field results

NASA Technical Reports Server (NTRS)

Slavin, J. A.; Tsurutani, B. T.; Smith, E. J.; Jones, D. E.; Sibeck, D. G.

1983-01-01

Magnetic field measurements from the first two passes of the ISEE-3 GEOTAIL Mission have been used to study the structure of the trans-lunar tail. Good agreement was found between the ISEE-3 magnetopause crossings and the Explorer 33, 35 model of Howe and Binsack (1972). Neutral sheet location was well ordered by the hinged current sheet models based upon near earth measurements. Between X = -20 and -120 earth radii the radius of the tail increases by about 30 percent while the lobe field strength decreases by approximately 60 percent. Beyond X = -100 to -1200 earth radii the tail diameter and lobe field magnitude become nearly constant at terminal values of approximately 60 earth radii and 9 nT, respectively. The distance at which the tail was observed to cease flaring, 100-120 earth radii, is in close agreement with the predictions of the analytic tail model of Coroniti and Kennel (1972). Overall, the findings of this study suggest that the magnetotail retains much of its near earth structure out to X = -220 earth radii.

Pitfalls in Prediction Modeling for Normal Tissue Toxicity in Radiation Therapy: An Illustration With the Individual Radiation Sensitivity and Mammary Carcinoma Risk Factor Investigation Cohorts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mbah, Chamberlain, E-mail: chamberlain.mbah@ugent.be; Department of Mathematical Modeling, Statistics, and Bioinformatics, Faculty of Bioscience Engineering, Ghent University, Ghent; Thierens, Hubert

Purpose: To identify the main causes underlying the failure of prediction models for radiation therapy toxicity to replicate. Methods and Materials: Data were used from two German cohorts, Individual Radiation Sensitivity (ISE) (n=418) and Mammary Carcinoma Risk Factor Investigation (MARIE) (n=409), of breast cancer patients with similar characteristics and radiation therapy treatments. The toxicity endpoint chosen was telangiectasia. The LASSO (least absolute shrinkage and selection operator) logistic regression method was used to build a predictive model for a dichotomized endpoint (Radiation Therapy Oncology Group/European Organization for the Research and Treatment of Cancer score 0, 1, or ≥2). Internal areas undermore » the receiver operating characteristic curve (inAUCs) were calculated by a naïve approach whereby the training data (ISE) were also used for calculating the AUC. Cross-validation was also applied to calculate the AUC within the same cohort, a second type of inAUC. Internal AUCs from cross-validation were calculated within ISE and MARIE separately. Models trained on one dataset (ISE) were applied to a test dataset (MARIE) and AUCs calculated (exAUCs). Results: Internal AUCs from the naïve approach were generally larger than inAUCs from cross-validation owing to overfitting the training data. Internal AUCs from cross-validation were also generally larger than the exAUCs, reflecting heterogeneity in the predictors between cohorts. The best models with largest inAUCs from cross-validation within both cohorts had a number of common predictors: hypertension, normalized total boost, and presence of estrogen receptors. Surprisingly, the effect (coefficient in the prediction model) of hypertension on telangiectasia incidence was positive in ISE and negative in MARIE. Other predictors were also not common between the 2 cohorts, illustrating that overcoming overfitting does not solve the problem of replication failure of prediction models completely. Conclusions: Overfitting and cohort heterogeneity are the 2 main causes of replication failure of prediction models across cohorts. Cross-validation and similar techniques (eg, bootstrapping) cope with overfitting, but the development of validated predictive models for radiation therapy toxicity requires strategies that deal with cohort heterogeneity.« less

Hearing the shape of the Ising model with a programmable superconducting-flux annealer.

PubMed

Vinci, Walter; Markström, Klas; Boixo, Sergio; Roy, Aidan; Spedalieri, Federico M; Warburton, Paul A; Severini, Simone

2014-07-16

Two objects can be distinguished if they have different measurable properties. Thus, distinguishability depends on the Physics of the objects. In considering graphs, we revisit the Ising model as a framework to define physically meaningful spectral invariants. In this context, we introduce a family of refinements of the classical spectrum and consider the quantum partition function. We demonstrate that the energy spectrum of the quantum Ising Hamiltonian is a stronger invariant than the classical one without refinements. For the purpose of implementing the related physical systems, we perform experiments on a programmable annealer with superconducting flux technology. Departing from the paradigm of adiabatic computation, we take advantage of a noisy evolution of the device to generate statistics of low energy states. The graphs considered in the experiments have the same classical partition functions, but different quantum spectra. The data obtained from the annealer distinguish non-isomorphic graphs via information contained in the classical refinements of the functions but not via the differences in the quantum spectra.

An evaluation of three two-dimensional computational fluid dynamics codes including low Reynolds numbers and transonic Mach numbers

NASA Technical Reports Server (NTRS)

Hicks, Raymond M.; Cliff, Susan E.

1991-01-01

Full-potential, Euler, and Navier-Stokes computational fluid dynamics (CFD) codes were evaluated for use in analyzing the flow field about airfoils sections operating at Mach numbers from 0.20 to 0.60 and Reynolds numbers from 500,000 to 2,000,000. The potential code (LBAUER) includes weakly coupled integral boundary layer equations for laminar and turbulent flow with simple transition and separation models. The Navier-Stokes code (ARC2D) uses the thin-layer formulation of the Reynolds-averaged equations with an algebraic turbulence model. The Euler code (ISES) includes strongly coupled integral boundary layer equations and advanced transition and separation calculations with the capability to model laminar separation bubbles and limited zones of turbulent separation. The best experiment/CFD correlation was obtained with the Euler code because its boundary layer equations model the physics of the flow better than the other two codes. An unusual reversal of boundary layer separation with increasing angle of attack, following initial shock formation on the upper surface of the airfoil, was found in the experiment data. This phenomenon was not predicted by the CFD codes evaluated.

String order parameters for one-dimensional Floquet symmetry protected topological phases

NASA Astrophysics Data System (ADS)

Kumar, Ajesh; Dumitrescu, Philipp T.; Potter, Andrew C.

2018-06-01

Floquet symmetry protected topological (FSPT) phases are nonequilibrium topological phases enabled by time-periodic driving. FSPT phases of one-dimensional (1D) chains of bosons, spins, or qubits host dynamically protected edge states that can store quantum information without decoherence, making them promising for use as quantum memories. While FSPT order cannot be detected by any local measurement, here we construct nonlocal string order parameters that directly measure general 1D FSPT order. We propose a superconducting-qubit array based realization of the simplest Ising FSPT phase, which can be implemented with existing quantum computing hardware. We devise an interferometric scheme to directly measure the nonlocal string order using only simple one- and two-qubit operations and single-qubit measurements.

Work Plan for Three-Dimensional Time-Varying, Hydrodynamic and Water Quality Model of Chesapeake Bay

DTIC Science & Technology

1988-08-01

successfully calibrated: a. Dissolved oxygen b. Anmonium c. Nitrate d . Dissolved inorganic phosphorus e. Silica f. Methane g. Sulfide Fluxes of dissolved...oxygen, amonium , nitrate , methane, and sulfide can be related to the rate of diagenesis. A less mechanistic, more empirical approach may be required...CLASSc;CA’ ON A ’I.ORITV 3 D.S1R RUT ON AVA LABMLTY OF REPORT ’b D LASPCTO1,DONGRANG C ED, kApproved for public rele~ise; distribution 2b DC~ASFAT.N

Quasi-two-dimensional spin correlations in the triangular lattice bilayer spin glass LuCoGaO 4

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fritsch, Katharina; Ross, Kathyrn A.; Granroth, Garrett E.

Here we present a single-crystal time-of-flight neutron scattering study of the static and dynamic spin correlations in LuCoGaO 4, a quasi-two-dimensional dilute triangular lattice antiferromagnetic spin-glass material. This system is based on Co 2+ ions that are randomly distributed on triangular bilayers within the YbFe 2O 4 type, hexagonal crystal structure. Antiferromagnetic short-range two-dimensional correlations at wave vectors Q = (1/3,1/3, L) develop within the bilayers at temperatures as high as |Θ CW| ~100 K and extend over roughly five unit cells at temperatures below T g = 19 K. These two-dimensional static correlations are observed as diffuse rods ofmore » neutron scattering intensity along c * and display a continuous spin freezing process in their energy dependence. Aside from exhibiting these typical spin-glass characteristics, this insulating material reveals a novel gapped magnetic resonant spin excitation at ΔE ~12 meV localized around Q = (1 / 3, 1 / 3,L) . The temperature dependence of the spin gap associated with this two-dimensional excitation correlates with the evolution of the static correlations into the spin-glass state ground state. Lastly, we associate it with the effect of the staggered exchange field acting on the S eff = 1/2 Ising-like doublet of the Co 2+ moments.« less

Quasi-two-dimensional spin correlations in the triangular lattice bilayer spin glass LuCoGaO 4

DOE PAGES

Fritsch, Katharina; Ross, Kathyrn A.; Granroth, Garrett E.; ...

2017-09-13

Here we present a single-crystal time-of-flight neutron scattering study of the static and dynamic spin correlations in LuCoGaO 4, a quasi-two-dimensional dilute triangular lattice antiferromagnetic spin-glass material. This system is based on Co 2+ ions that are randomly distributed on triangular bilayers within the YbFe 2O 4 type, hexagonal crystal structure. Antiferromagnetic short-range two-dimensional correlations at wave vectors Q = (1/3,1/3, L) develop within the bilayers at temperatures as high as |Θ CW| ~100 K and extend over roughly five unit cells at temperatures below T g = 19 K. These two-dimensional static correlations are observed as diffuse rods ofmore » neutron scattering intensity along c * and display a continuous spin freezing process in their energy dependence. Aside from exhibiting these typical spin-glass characteristics, this insulating material reveals a novel gapped magnetic resonant spin excitation at ΔE ~12 meV localized around Q = (1 / 3, 1 / 3,L) . The temperature dependence of the spin gap associated with this two-dimensional excitation correlates with the evolution of the static correlations into the spin-glass state ground state. Lastly, we associate it with the effect of the staggered exchange field acting on the S eff = 1/2 Ising-like doublet of the Co 2+ moments.« less

Ground-state and magnetocaloric properties of a coupled spin-electron double-tetrahedral chain (exact study at the half filling)

NASA Astrophysics Data System (ADS)

Gálisová, Lucia; Jakubczyk, Dorota

2017-01-01

Ground-state and magnetocaloric properties of a double-tetrahedral chain, in which nodal lattice sites occupied by the localized Ising spins regularly alternate with triangular clusters half filled with mobile electrons, are exactly investigated by using the transfer-matrix method in combination with the construction of the Nth tensor power of the discrete Fourier transformation. It is shown that the ground state of the model is formed by two non-chiral phases with the zero residual entropy and two chiral phases with the finite residual entropy S = NkB ln 2. Depending on the character of the exchange interaction between the localized Ising spins and mobile electrons, one or three magnetization plateaus can be observed in the magnetization process. Their heights basically depend on the values of Landé g-factors of the Ising spins and mobile electrons. It is also evidenced that the system exhibits both the conventional and inverse magnetocaloric effect depending on values of the applied magnetic field and temperature.

Ising game: Nonequilibrium steady states of resource-allocation systems

NASA Astrophysics Data System (ADS)

Xin, C.; Yang, G.; Huang, J. P.

2017-04-01

Resource-allocation systems are ubiquitous in the human society. But how external fields affect the state of such systems remains poorly explored due to the lack of a suitable model. Because the behavior of spins pursuing energy minimization required by physical laws is similar to that of humans chasing payoff maximization studied in game theory, here we combine the Ising model with the market-directed resource-allocation game, yielding an Ising game. Based on the Ising game, we show theoretical, simulative and experimental evidences for a formula, which offers a clear expression of nonequilibrium steady states (NESSs). Interestingly, the formula also reveals a convertible relationship between the external field (exogenous factor) and resource ratio (endogenous factor), and a class of saturation as the external field exceeds certain limits. This work suggests that the Ising game could be a suitable model for studying external-field effects on resource-allocation systems, and it could provide guidance both for seeking more relations between NESSs and equilibrium states and for regulating human systems by choosing NESSs appropriately.

On the use of a sunward-libration-point orbiting spacecraft as an IMF monitor for magnetospheric studies

NASA Technical Reports Server (NTRS)

Kelly, T. J.; Crooker, N. U.; Siscoe, G. L.; Russell, C. T.; Smith, E. J.

1984-01-01

Magnetospheric studies often require knowledge of the orientation of the IMF. In order to test the accuracy of using magnetometer data from a spacecraft orbiting the sunward libration point for this purpose, the angle between the IMF at ISEE 3, when it was positioned around the libration point, and at ISEE 1, orbiting Earth, has been calculated for a data set of two-hour periods covering four months. For each period, a ten-minute average of ISEE 1 data is compared with ten-minute averages of ISEE 3 data at successively lagged intervals. At the lag time equal to the time required for the solar wind to convect from ISEE 3 to ISEE 1, the median angle between the IMF orientation at the two spacecraft is 20 deg, and 80% of the cases have angles less than 38 deg. The results for the angles projected on the y-z plane are essentially the same.

Universal Off-Equilibrium Scaling of Critical Cumulants in the QCD Phase Diagram

DOE PAGES

Mukherjee, Swagato; Venugopalan, Raju; Yin, Yi

2016-11-23

Exploiting the universality between the QCD critical point and the three-dimensional Ising model, closed form expressions derived for nonequilibrium critical cumulants on the crossover side of the critical point reveal that they can differ in both magnitude and sign from equilibrium expectations. Here, we demonstrate here that key elements of the Kibble-Zurek framework of nonequilibrium phase transitions can be employed to describe the dynamics of these critical cumulants. Lastly, our results suggest that observables sensitive to critical dynamics in heavy-ion collisions should be expressible as universal scaling functions, thereby providing powerful model-independent guidance in searches for the QCD critical point.

Rhythmic behavior in a two-population mean-field Ising model

NASA Astrophysics Data System (ADS)

Collet, Francesca; Formentin, Marco; Tovazzi, Daniele

2016-10-01

Many real systems composed of a large number of interacting components, as, for instance, neural networks, may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic oscillations are indeed one of the most common self-organized behavior observed in living systems. In the present paper we study some dynamical features of a two-population generalization of the mean-field Ising model with the scope of investigating simple mechanisms capable to generate rhythms in large groups of interacting individuals. We show that the system may undergo a transition from a disordered phase, where the magnetization of each population fluctuates closely around zero, to a phase in which they both display a macroscopic regular rhythm. In particular, there exists a region in the parameter space where having two groups of spins with inter- and intrapopulation interactions of different strengths suffices for the emergence of a robust periodic behavior.

Physics and financial economics (1776-2014): puzzles, Ising and agent-based models.

PubMed

Sornette, Didier

2014-06-01

This short review presents a selected history of the mutual fertilization between physics and economics--from Isaac Newton and Adam Smith to the present. The fundamentally different perspectives embraced in theories developed in financial economics compared with physics are dissected with the examples of the volatility smile and of the excess volatility puzzle. The role of the Ising model of phase transitions to model social and financial systems is reviewed, with the concepts of random utilities and the logit model as the analog of the Boltzmann factor in statistical physics. Recent extensions in terms of quantum decision theory are also covered. A wealth of models are discussed briefly that build on the Ising model and generalize it to account for the many stylized facts of financial markets. A summary of the relevance of the Ising model and its extensions is provided to account for financial bubbles and crashes. The review would be incomplete if it did not cover the dynamical field of agent-based models (ABMs), also known as computational economic models, of which the Ising-type models are just special ABM implementations. We formulate the 'Emerging Intelligence Market Hypothesis' to reconcile the pervasive presence of 'noise traders' with the near efficiency of financial markets. Finally, we note that evolutionary biology, more than physics, is now playing a growing role to inspire models of financial markets.

Physics and financial economics (1776-2014): puzzles, Ising and agent-based models

NASA Astrophysics Data System (ADS)

Sornette, Didier

2014-06-01

This short review presents a selected history of the mutual fertilization between physics and economics—from Isaac Newton and Adam Smith to the present. The fundamentally different perspectives embraced in theories developed in financial economics compared with physics are dissected with the examples of the volatility smile and of the excess volatility puzzle. The role of the Ising model of phase transitions to model social and financial systems is reviewed, with the concepts of random utilities and the logit model as the analog of the Boltzmann factor in statistical physics. Recent extensions in terms of quantum decision theory are also covered. A wealth of models are discussed briefly that build on the Ising model and generalize it to account for the many stylized facts of financial markets. A summary of the relevance of the Ising model and its extensions is provided to account for financial bubbles and crashes. The review would be incomplete if it did not cover the dynamical field of agent-based models (ABMs), also known as computational economic models, of which the Ising-type models are just special ABM implementations. We formulate the ‘Emerging Intelligence Market Hypothesis’ to reconcile the pervasive presence of ‘noise traders’ with the near efficiency of financial markets. Finally, we note that evolutionary biology, more than physics, is now playing a growing role to inspire models of financial markets.

Correspondence between spanning trees and the Ising model on a square lattice

NASA Astrophysics Data System (ADS)

Viswanathan, G. M.

2017-06-01

An important problem in statistical physics concerns the fascinating connections between partition functions of lattice models studied in equilibrium statistical mechanics on the one hand and graph theoretical enumeration problems on the other hand. We investigate the nature of the relationship between the number of spanning trees and the partition function of the Ising model on the square lattice. The spanning tree generating function T (z ) gives the spanning tree constant when evaluated at z =1 , while giving the lattice green function when differentiated. It is known that for the infinite square lattice the partition function Z (K ) of the Ising model evaluated at the critical temperature K =Kc is related to T (1 ) . Here we show that this idea in fact generalizes to all real temperatures. We prove that [Z(K ) s e c h 2 K ] 2=k exp[T (k )] , where k =2 tanh(2 K )s e c h (2 K ) . The identical Mahler measure connects the two seemingly disparate quantities T (z ) and Z (K ) . In turn, the Mahler measure is determined by the random walk structure function. Finally, we show that the the above correspondence does not generalize in a straightforward manner to nonplanar lattices.

I. Excluded volume effects in Ising cluster distributions and nuclear multifragmentation. II. Multiple-chance effects in alpha-particle evaporation

NASA Astrophysics Data System (ADS)

Breus, Dimitry Eugene

In Part I, geometric clusters of the Ising model are studied as possible model clusters for nuclear multifragmentation. These clusters may not be considered as non-interacting (ideal gas) due to excluded volume effect which predominantly is the artifact of the cluster's finite size. Interaction significantly complicates the use of clusters in the analysis of thermodynamic systems. Stillinger's theory is used as a basis for the analysis, which within the RFL (Reiss, Frisch, Lebowitz) fluid-of-spheres approximation produces a prediction for cluster concentrations well obeyed by geometric clusters of the Ising model. If thermodynamic condition of phase coexistence is met, these concentrations can be incorporated into a differential equation procedure of moderate complexity to elucidate the liquid-vapor phase diagram of the system with cluster interaction included. The drawback of increased complexity is outweighted by the reward of greater accuracy of the phase diagram, as it is demonstrated by the Ising model. A novel nuclear-cluster analysis procedure is developed by modifying Fisher's model to contain cluster interaction and employing the differential equation procedure to obtain thermodynamic variables. With this procedure applied to geometric clusters, the guidelines are developed to look for excluded volume effect in nuclear multifragmentation. In Part II, an explanation is offered for the recently observed oscillations in the energy spectra of alpha-particles emitted from hot compound nuclei. Contrary to what was previously expected, the oscillations are assumed to be caused by the multiple-chance nature of alpha-evaporation. In a semi-empirical fashion this assumption is successfully confirmed by a technique of two-spectra decomposition which treats experimental alpha-spectra as having contributions from at least two independent emitters. Building upon the success of the multiple-chance explanation of the oscillations, Moretto's single-chance evaporation theory is augmented to include multiple-chance emission and tested on experimental data to yield positive results.

de Almeida-Thouless instability in short-range Ising spin glasses

NASA Astrophysics Data System (ADS)

Singh, R. R. P.; Young, A. P.

2017-07-01

We use high-temperature series expansions to study the ±J Ising spin glass in a magnetic field in d -dimensional hypercubic lattices for d =5 -8 and in the infinite-range Sherrington-Kirkpatrick (SK) model. The expansions are obtained in the variable w =tanh2J /T for arbitrary values of u =tanh2h /T complete to order w10. We find that the scaling dimension Δ associated with the ordering-field h2 equals 2 in the SK model and for d ≥6 . However, in agreement with the work of Fisher and Sompolinsky [Phys. Rev. Lett. 54, 1063 (1985), 10.1103/PhysRevLett.54.1063], there is a violation of scaling in a finite field, leading to an anomalous h -T dependence of the de Almeida-Thouless (AT) [J. Phys. A 11, 983 (1978), 10.1088/0305-4470/11/5/028] line in high dimensions, whereas scaling is restored as d →6 . Within the convergence of our series analysis, we present evidence supporting an AT line in d ≥6 . In d =5 , the exponents γ and Δ are substantially larger than mean-field values, but we do not see clear evidence for the AT line in d =5 .

Kinetic Monte Carlo Simulations of Rod Eutectics and the Surface Roughening Transition in Binary Alloys

NASA Technical Reports Server (NTRS)

Bentz, Daniel N.; Betush, William; Jackson, Kenneth A.

2003-01-01

In this paper we report on two related topics: Kinetic Monte Carlo simulations of the steady state growth of rod eutectics from the melt, and a study of the surface roughness of binary alloys. We have implemented a three dimensional kinetic Monte Carlo (kMC) simulation with diffusion by pair exchange only in the liquid phase. Entropies of fusion are first chosen to fit the surface roughness of the pure materials, and the bond energies are derived from the equilibrium phase diagram, by treating the solid and liquid as regular and ideal solutions respectively. A simple cubic lattice oriented in the {100} direction is used. Growth of the rods is initiated from columns of pure B material embedded in an A matrix, arranged in a close packed array with semi-periodic boundary conditions. The simulation cells typically have dimensions of 50 by 87 by 200 unit cells. Steady state growth is compliant with the Jackson-Hunt model. In the kMC simulations, using the spin-one Ising model, growth of each phase is faceted or nonfaceted phases depending on the entropy of fusion. There have been many studies of the surface roughening transition in single component systems, but none for binary alloy systems. The location of the surface roughening transition for the phases of a eutectic alloy determines whether the eutectic morphology will be regular or irregular. We have conducted a study of surface roughness on the spin-one Ising Model with diffusion using kMC. The surface roughness was found to scale with the melting temperature of the alloy as given by the liquidus line on the equilibrium phase diagram. The density of missing lateral bonds at the surface was used as a measure of surface roughness.

Emergent equilibrium in many-body optical bistability

NASA Astrophysics Data System (ADS)

Foss-Feig, Michael; Niroula, Pradeep; Young, Jeremy; Hafezi, Mohammad; Gorshkov, Alexey; Wilson, Ryan; Maghrebi, Mohammad

2017-04-01

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to Rydberg gases, establishing a fascinating interface between traditional many-body physics and the non-equilibrium setting of cavity-QED. At this interface the standard intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. We study the driven-dissipative Bose-Hubbard model, a minimal description of atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability-a foundational and patently non-equilibrium model of cavity-QED-the steady state possesses an emergent equilibrium description in terms of an Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model. M.F.M., J.T.Y., and A.V.G. acknowledge support by ARL CDQI, ARO MURI, NSF QIS, ARO, NSF PFC at JQI, and AFOSR. R.M.W. acknowledges partial support from the NSF under Grant No. PHYS-1516421. M.H. acknowledges support by AFOSR-MURI, ONR and Sloan Foundation.

Bipartite charge fluctuations in one-dimensional Z2 superconductors and insulators

NASA Astrophysics Data System (ADS)

Herviou, Loïc; Mora, Christophe; Le Hur, Karyn

2017-09-01

Bipartite charge fluctuations (BCFs) have been introduced to provide an experimental indication of many-body entanglement. They have proved themselves to be a very efficient and useful tool to characterize quantum phase transitions in a variety of quantum models conserving the total number of particles (or magnetization for spin systems) and can be measured experimentally. We study the BCFs in generic one-dimensional Z2 (topological) models including the Kitaev superconducting wire model, the Ising chain, or various topological insulators such as the Su-Schrieffer-Heeger model. The considered charge (either the fermionic number or the relative density) is no longer conserved, leading to macroscopic fluctuations of the number of particles. We demonstrate that at phase transitions characterized by a linear dispersion, the BCFs probe the change in a winding number that allows one to pinpoint the transition and corresponds to the topological invariant for standard models. Additionally, we prove that a subdominant logarithmic contribution is still present at the exact critical point. Its quantized coefficient is universal and characterizes the critical model. Results are extended to the Rashba topological nanowires and to the X Y Z model.

Phase transitions in Ising models on directed networks

NASA Astrophysics Data System (ADS)

Lipowski, Adam; Ferreira, António Luis; Lipowska, Dorota; Gontarek, Krzysztof

2015-11-01

We examine Ising models with heat-bath dynamics on directed networks. Our simulations show that Ising models on directed triangular and simple cubic lattices undergo a phase transition that most likely belongs to the Ising universality class. On the directed square lattice the model remains paramagnetic at any positive temperature as already reported in some previous studies. We also examine random directed graphs and show that contrary to undirected ones, percolation of directed bonds does not guarantee ferromagnetic ordering. Only above a certain threshold can a random directed graph support finite-temperature ferromagnetic ordering. Such behavior is found also for out-homogeneous random graphs, but in this case the analysis of magnetic and percolative properties can be done exactly. Directed random graphs also differ from undirected ones with respect to zero-temperature freezing. Only at low connectivity do they remain trapped in a disordered configuration. Above a certain threshold, however, the zero-temperature dynamics quickly drives the model toward a broken symmetry (magnetized) state. Only above this threshold, which is almost twice as large as the percolation threshold, do we expect the Ising model to have a positive critical temperature. With a very good accuracy, the behavior on directed random graphs is reproduced within a certain approximate scheme.

Digital quantum simulators in a scalable architecture of hybrid spin-photon qubits

PubMed Central

Chiesa, Alessandro; Santini, Paolo; Gerace, Dario; Raftery, James; Houck, Andrew A.; Carretta, Stefano

2015-01-01

Resolving quantum many-body problems represents one of the greatest challenges in physics and physical chemistry, due to the prohibitively large computational resources that would be required by using classical computers. A solution has been foreseen by directly simulating the time evolution through sequences of quantum gates applied to arrays of qubits, i.e. by implementing a digital quantum simulator. Superconducting circuits and resonators are emerging as an extremely promising platform for quantum computation architectures, but a digital quantum simulator proposal that is straightforwardly scalable, universal, and realizable with state-of-the-art technology is presently lacking. Here we propose a viable scheme to implement a universal quantum simulator with hybrid spin-photon qubits in an array of superconducting resonators, which is intrinsically scalable and allows for local control. As representative examples we consider the transverse-field Ising model, a spin-1 Hamiltonian, and the two-dimensional Hubbard model and we numerically simulate the scheme by including the main sources of decoherence. PMID:26563516

Domain-wall excitations in the two-dimensional Ising spin glass

NASA Astrophysics Data System (ADS)

Khoshbakht, Hamid; Weigel, Martin

2018-02-01

The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient implementations of combinatorial optimization algorithms to determine exact ground states for systems on square lattices with up to 10 000 ×10 000 spins. While these mappings only work for planar graphs, for example for systems with periodic boundary conditions in at most one direction, we suggest here an iterative windowing technique that allows one to determine ground states for fully periodic samples up to sizes similar to those for the open-periodic case. Based on these techniques, a large number of disorder samples are used together with a careful finite-size scaling analysis to determine the stiffness exponents and domain-wall fractal dimensions with unprecedented accuracy, our best estimates being θ =-0.2793 (3 ) and df=1.273 19 (9 ) for Gaussian couplings. For bimodal disorder, a new uniform sampling algorithm allows us to study the domain-wall fractal dimension, finding df=1.279 (2 ) . Additionally, we also investigate the distributions of ground-state energies, of domain-wall energies, and domain-wall lengths.

Exact sampling hardness of Ising spin models

NASA Astrophysics Data System (ADS)

Fefferman, B.; Foss-Feig, M.; Gorshkov, A. V.

2017-09-01

We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of exact classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.

The Influence of Informal Science Education Experiences on the Development of Two Beginning Teachers' Science Classroom Teaching Identity

NASA Astrophysics Data System (ADS)

Katz, Phyllis; Randy McGinnis, J.; Riedinger, Kelly; Marbach-Ad, Gili; Dai, Amy

2013-12-01

In case studies of two first-year elementary classroom teachers, we explored the influence of informal science education (ISE) they experienced in their teacher education program. Our theoretical lens was identity development, delimited to classroom science teaching. We used complementary data collection methods and analysis, including interviews, electronic communications, and drawing prompts. We found that our two participants referenced as important the ISE experiences in their development of classroom science identities that included resilience, excitement and engagement in science teaching and learning-qualities that are emphasized in ISE contexts. The data support our conclusion that the ISE experiences proved especially memorable to teacher education interns during the implementation of the No Child Left Behind policy which concentrated on school-tested subjects other than science.

The ISEE-1 and ISEE-2 plasma wave investigation

NASA Technical Reports Server (NTRS)

Gurnett, D. A.; Scarf, F. L.; Fredricks, R. W.; Smith, E. J.

1978-01-01

The ISEE-1 and ISEE-2 plasma wave experiments are designed to provide basic information on wave-particle interactions in the earth's magnetosphere and in the solar wind. The ISEE-1 plasma wave instrument uses three electric dipole antennas with lengths of 215, 73.5 and 0.61 m for electric field measurements, and a triaxial search coil antenna for magnetic field measurements. The ISEE-2 instrument uses two electric dipole antennas with lengths of 30 and 0.61 m for electric field measurements and a single-axis search coil antenna for magnetic field measurements. The primary scientific objectives of the experiments are described, including the resolution of space-time relationships of plasma wave phenomena and VLBI studies. The instrumentation is described, with emphasis on the antennas and the electronics.

Massively parallel multicanonical simulations

NASA Astrophysics Data System (ADS)

Gross, Jonathan; Zierenberg, Johannes; Weigel, Martin; Janke, Wolfhard

2018-03-01

Generalized-ensemble Monte Carlo simulations such as the multicanonical method and similar techniques are among the most efficient approaches for simulations of systems undergoing discontinuous phase transitions or with rugged free-energy landscapes. As Markov chain methods, they are inherently serial computationally. It was demonstrated recently, however, that a combination of independent simulations that communicate weight updates at variable intervals allows for the efficient utilization of parallel computational resources for multicanonical simulations. Implementing this approach for the many-thread architecture provided by current generations of graphics processing units (GPUs), we show how it can be efficiently employed with of the order of 104 parallel walkers and beyond, thus constituting a versatile tool for Monte Carlo simulations in the era of massively parallel computing. We provide the fully documented source code for the approach applied to the paradigmatic example of the two-dimensional Ising model as starting point and reference for practitioners in the field.

Correlated lateral phase separations in stacks of lipid membranes

NASA Astrophysics Data System (ADS)

Hoshino, Takuma; Komura, Shigeyuki; Andelman, David

2015-12-01

Motivated by the experimental study of Tayebi et al. [Nat. Mater. 11, 1074 (2012)] on phase separation of stacked multi-component lipid bilayers, we propose a model composed of stacked two-dimensional Ising spins. We study both its static and dynamical features using Monte Carlo simulations with Kawasaki spin exchange dynamics that conserves the order parameter. We show that at thermodynamical equilibrium, due to strong inter-layer correlations, the system forms a continuous columnar structure for any finite interaction across adjacent layers. Furthermore, the phase separation shows a faster dynamics as the inter-layer interaction is increased. This temporal behavior is mainly due to an effective deeper temperature quench because of the larger value of the critical temperature, Tc, for larger inter-layer interaction. When the temperature ratio, T/Tc, is kept fixed, the temporal growth exponent does not increase and even slightly decreases as a function of the increased inter-layer interaction.

Bootstrapping conformal field theories with the extremal functional method.

PubMed

El-Showk, Sheer; Paulos, Miguel F

2013-12-13

The existence of a positive linear functional acting on the space of (differences between) conformal blocks has been shown to rule out regions in the parameter space of conformal field theories (CFTs). We argue that at the boundary of the allowed region the extremal functional contains, in principle, enough information to determine the dimensions and operator product expansion (OPE) coefficients of an infinite number of operators appearing in the correlator under analysis. Based on this idea we develop the extremal functional method (EFM), a numerical procedure for deriving the spectrum and OPE coefficients of CFTs lying on the boundary (of solution space). We test the EFM by using it to rederive the low lying spectrum and OPE coefficients of the two-dimensional Ising model based solely on the dimension of a single scalar quasiprimary--no Virasoro algebra required. Our work serves as a benchmark for applications to more interesting, less known CFTs in the near future.

A pentacene monolayer trapped between graphene and a substrate.

PubMed

Zhang, Qicheng; Peng, Boyu; Chan, Paddy Kwok Leung; Luo, Zhengtang

2015-09-21

A self-assembled pentacene monolayer can be fabricated between the solid-solid interface of few-layered graphene (FLG) and the mica substrate, through a diffusion-spreading method. By utilizing a transfer method that allows us to sandwich pentacene between graphene and mica, followed by controlled annealing, we enabled the diffused pentacene to be trapped in the interfaces and led to the formation of a stable monolayer. We found that the formation of a monolayer is kinetically favored by using a 2D Ising lattice gas model for pentacene trapped between the graphene-substrate interfaces. This kinetic Monte Carlo simulation results indicate that, due to the graphene substrate enclosure, the spreading of the first layer proceeds faster than the second layer, as the kinetics favors the filling of voids by molecules from the second layer. This graphene assisted monolayer assembly method provides a new avenue for the fabrication of two-dimensional monolayer structures.

Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization

NASA Astrophysics Data System (ADS)

Classen, Laura; Herbut, Igor F.; Janssen, Lukas; Scherer, Michael M.

2016-03-01

We study the competition of spin- and charge-density waves and their quantum multicritical behavior for the semimetal-insulator transitions of low-dimensional Dirac fermions. Employing the effective Gross-Neveu-Yukawa theory with two order parameters as a model for graphene and a growing number of other two-dimensional Dirac materials allows us to describe the physics near the multicritical point at which the semimetallic and the spin- and charge-density-wave phases meet. With the help of a functional renormalization group approach, we are able to reveal a complex structure of fixed points, the stability properties of which decisively depend on the number of Dirac fermions Nf. We give estimates for the critical exponents and observe crucial quantitative corrections as compared to the previous first-order ɛ expansion. For small Nf, the universal behavior near the multicritical point is determined by the chiral Heisenberg universality class supplemented by a decoupled, purely bosonic, Ising sector. At large Nf, a novel fixed point with nontrivial couplings between all sectors becomes stable. At intermediate Nf, including the graphene case (Nf=2 ), no stable and physically admissible fixed point exists. Graphene's phase diagram in the vicinity of the intersection between the semimetal, antiferromagnetic, and staggered density phases should consequently be governed by a triple point exhibiting first-order transitions.

Small-cluster renormalization group in Ising and Blume-Emery-Griffiths models with ferromagnetic, antiferromagnetic, and quenched disordered magnetic interactions

NASA Astrophysics Data System (ADS)

Antenucci, F.; Crisanti, A.; Leuzzi, L.

2014-07-01

The Ising and Blume-Emery-Griffiths (BEG) models' critical behavior is analyzed in two dimensions and three dimensions by means of a renormalization group scheme on small clusters made of a few lattice cells. Different kinds of cells are proposed for both ordered and disordered model cases. In particular, cells preserving a possible antiferromagnetic ordering under renormalization allow for the determination of the Néel critical point and its scaling indices. These also provide more reliable estimates of the Curie fixed point than those obtained using cells preserving only the ferromagnetic ordering. In all studied dimensions, the present procedure does not yield a strong-disorder critical point corresponding to the transition to the spin-glass phase. This limitation is thoroughly analyzed and motivated.

Emergent long-range synchronization of oscillating ecological populations without external forcing described by Ising universality

PubMed Central

Noble, Andrew E.; Machta, Jonathan; Hastings, Alan

2015-01-01

Understanding the synchronization of oscillations across space is fundamentally important to many scientific disciplines. In ecology, long-range synchronization of oscillations in spatial populations may elevate extinction risk and signal an impending catastrophe. The prevailing assumption is that synchronization on distances longer than the dispersal scale can only be due to environmental correlation (the Moran effect). In contrast, we show how long-range synchronization can emerge over distances much longer than the length scales of either dispersal or environmental correlation. In particular, we demonstrate that the transition from incoherence to long-range synchronization of two-cycle oscillations in noisy spatial population models is described by the Ising universality class of statistical physics. This result shows, in contrast to all previous work, how the Ising critical transition can emerge directly from the dynamics of ecological populations. PMID:25851364

Ferromagnetic transition in a simple variant of the Ising model on multiplex networks

NASA Astrophysics Data System (ADS)

Krawiecki, A.

2018-02-01

Multiplex networks consist of a fixed set of nodes connected by several sets of edges which are generated separately and correspond to different networks ("layers"). Here, a simple variant of the Ising model on multiplex networks with two layers is considered, with spins located in the nodes and edges corresponding to ferromagnetic interactions between them. Critical temperatures for the ferromagnetic transition are evaluated for the layers in the form of random Erdös-Rényi graphs or heterogeneous scale-free networks using the mean-field approximation and the replica method, from the replica symmetric solution. Both methods require the use of different "partial" magnetizations, associated with different layers of the multiplex network, and yield qualitatively similar results. If the layers are strongly heterogeneous the critical temperature differs noticeably from that for the Ising model on a network being a superposition of the two layers, evaluated in the mean-field approximation neglecting the effect of the underlying multiplex structure on the correlations between the degrees of nodes. The critical temperature evaluated from the replica symmetric solution depends sensitively on the correlations between the degrees of nodes in different layers and shows satisfactory quantitative agreement with that obtained from Monte Carlo simulations. The critical behavior of the magnetization for the model with strongly heterogeneous layers can depend on the distributions of the degrees of nodes and is then determined by the properties of the most heterogeneous layer.

The NASA Radiation Interuniversity Science and Engineering(RaISE) Project: A Model for Inter-collaboration and Distance Learning in Radiation Physics and Nuclear Engineering

NASA Technical Reports Server (NTRS)

Denkins, Pamela S.; Saganti, P.; Obot, V.; Singleterry, R.

2006-01-01

This viewgraph document reviews the Radiation Interuniversity Science and Engineering (RaISE) Project, which is a project that has as its goals strengthening and furthering the curriculum in radiation sciences at two Historically Black Colleges and Universities (HBCU), Prairie View A&M University and Texas Southern University. Those were chosen in part because of the proximity to NASA Johnson Space Center, a lead center for the Space Radiation Health Program. The presentation reviews the courses that have been developed, both in-class, and on-line.

Magnetic quasi-long-range ordering in nematic systems due to competition between higher-order couplings

NASA Astrophysics Data System (ADS)

Žukovič, Milan; Kalagov, Georgii

2018-05-01

Critical properties of the two-dimensional X Y model involving solely nematic-like terms of the second and third orders are investigated by spin-wave analysis and Monte Carlo simulation. It is found that, even though neither of the nematic-like terms alone can induce magnetic ordering, their coexistence and competition leads to an extended phase of the magnetic quasi-long-range-order phase, wedged between the two nematic-like phases induced by the respective couplings. Thus, except for the multicritical point, at which all the phases meet, for any finite value of the coupling parameters ratio there are two phase transition: one from the paramagnetic phase to one of the two nematic-like phases followed by another one at lower temperatures to the magnetic phase. The finite-size scaling analysis indicates that the phase transitions between the magnetic and nematic-like phases belong to the Ising and three-state Potts universality classes. Inside the competition-induced algebraic magnetic phase, the spin-pair correlation function is found to decay even much more slowly than in the standard X Y model with purely magnetic interactions. Such a magnetic phase is characterized by an extremely low vortex-antivortex pair density attaining a minimum close to the point at which the two couplings are of about equal strength.

Ginzburg criterion for ionic fluids: the effect of Coulomb interactions.

PubMed

Patsahan, O

2013-08-01

The effect of the Coulomb interactions on the crossover between mean-field and Ising critical behavior in ionic fluids is studied using the Ginzburg criterion. We consider the charge-asymmetric primitive model supplemented by short-range attractive interactions in the vicinity of the gas-liquid critical point. The model without Coulomb interactions exhibiting typical Ising critical behavior is used to calibrate the Ginzburg temperature of the systems comprising electrostatic interactions. Using the collective variables method, we derive a microscopic-based effective Hamiltonian for the full model. We obtain explicit expressions for all the relevant Hamiltonian coefficients within the framework of the same approximation, i.e., the one-loop approximation. Then we consistently calculate the reduced Ginzburg temperature t(G) for both the purely Coulombic model (a restricted primitive model) and the purely nonionic model (a hard-sphere square-well model) as well as for the model parameters ranging between these two limiting cases. Contrary to the previous theoretical estimates, we obtain the reduced Ginzburg temperature for the purely Coulombic model to be about 20 times smaller than for the nonionic model. For the full model including both short-range and long-range interactions, we show that t(G) approaches the value found for the purely Coulombic model when the strength of the Coulomb interactions becomes sufficiently large. Our results suggest a key role of Coulomb interactions in the crossover behavior observed experimentally in ionic fluids as well as confirm the Ising-like criticality in the Coulomb-dominated ionic systems.

A study of the temporal and spectral characteristics of gamma ray bursts. Ph.D. Thesis - Maryland Univ.

NASA Technical Reports Server (NTRS)

Norris, J.

1983-01-01

Gamma-ray burst data obtained from the ISEE-3 Gamma Ray Burst Spectrometer and the Solar Maximum Mission's Hard X-ray Burst Spectrometer (HXRBS) were analyzed to yield information on burst temporal and spectral characteristics. A Monte Carlo approach was used to simulate the HXRBS response to candidate spectral models. At energies above about 100 keV, the spectra are well fit by exponential forms. At lower energies, 30 keV to 60 keV, depressions below the model continua are apparent in some bursts. The depressions are not instrumental or data-reduction artifacts. The event selection criterion of the ISEE-3 experiment is based on the time to accumulate a present number of photons rather than the photon count per unit time and is consequently independent of event duration for a given burst intensity, unlike most conventional systems. As a result, a significantly greater percentage of fast, narrow events have been detected. The ratio of count rates from two ISEE-3 detectors indicates that bursts with durations or approx. one second have much softer spectra than longer bursts.

Critical behavior of the order-disorder phase transition in β -brass investigated by x-ray scattering

NASA Astrophysics Data System (ADS)

Madsen, A.; Als-Nielsen, J.; Hallmann, J.; Roth, T.; Lu, W.

2016-07-01

β -brass exhibits an archetypical example of an order-disorder transition with a critical behavior that was previously investigated by neutron scattering. The data were well described by the three-dimensional (3d) Ising model but the relatively crude experimental resolution prevented an in-depth examination of the single-length scaling hypothesis, a cornerstone in the theory of critical phenomena. With the development of synchrotron x-ray experiments, high-resolution data could be recorded and surprisingly it was found that the single-length scaling did not hold in most critical systems, possibly due to strain originating from surface defects and/or impurities. In this paper we demonstrate single-length critical behavior using high-resolution x-ray scattering in β -brass. The investigations confirm that β -brass behaves like a 3d Ising system over a wide range of length scales comprising correlated clusters of millions of atoms. To vary the surface sensitivity, experiments have been performed both in Bragg reflection and Laue transmission geometries but without any substantial differences observed in the scaling and critical behavior.

Tests of conformal field theory at the Yang-Lee singularity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wydro, Tomasz; McCabe, John F.

2009-12-14

This paper studies the Yang-Lee edge singularity of 2-dimensional (2D) Ising model based on a quantum spin chain and transfer matrix measurements on the cylinder. Based on finite-size scaling, the low-lying excitation spectrum is found at the Yang-Lee edge singularity. Based on transfer matrix techniques, the single structure constant is evaluated at the Yang-Lee edge singularity. The results of both types of measurements are found to be fully consistent with the predictions for the (A{sub 4}, A{sub 1}) minimal conformal field theory, which was previously identified with this critical point.

Relationship between the transverse-field Ising model and the X Y model via the rotating-wave approximation

NASA Astrophysics Data System (ADS)

Kiely, Thomas G.; Freericks, J. K.

2018-02-01

In a large transverse field, there is an energy cost associated with flipping spins along the axis of the field. This penalty can be employed to relate the transverse-field Ising model in a large field to the X Y model in no field (when measurements are performed at the proper stroboscopic times). We describe the details for how this relationship works and, in particular, we also show under what circumstances it fails. We examine wave-function overlap between the two models and observables, such as spin-spin Green's functions. In general, the mapping is quite robust at short times, but will ultimately fail if the run time becomes too long. There is also a tradeoff between the length of time one can run a simulation out to and the time jitter of the stroboscopic measurements that must be balanced when planning to employ this mapping.

Ising antiferromagnet on a finite triangular lattice with free boundary conditions

NASA Astrophysics Data System (ADS)

Kim, Seung-Yeon

2015-11-01

The exact integer values for the density of states of the Ising model on an equilateral triangular lattice with free boundary conditions are evaluated up to L = 24 spins on a side for the first time by using the microcanonical transfer matrix. The total number of states is 2 N s = 2300 ≈ 2.037 × 1090 for L = 24, where N s = L( L+1)/2 is the number of spins. Classifying all 2300 spin states according to their energy values is an enormous work. From the density of states, the exact partition function zeros in the complex temperature plane of the triangular-lattice Ising model are evaluated. Using the density of states and the partition function zeros, we investigate the properties of the triangularlattice Ising antiferromagnet. The scaling behavior of the ground-state entropy and the form of the correlation length at T = 0 are studied for the triangular-lattice Ising antiferromagnet with free boundary conditions. Also, the scaling behavior of the Fisher edge singularity is investigated.

Distinct nature of orbital-selective Mott phases dominated by low-energy local spin fluctuations

NASA Astrophysics Data System (ADS)

Song, Ze-Yi; Jiang, Xiu-Cai; Lin, Hai-Qing; Zhang, Yu-Zhong

2017-12-01

Quantum orbital-selective Mott (OSM) transitions are investigated within dynamical mean-field theory based on a two-orbital Hubbard model with different bandwidth at half filling. We find two distinct OSM phases both showing coexistence of itinerant electrons and localized spins, dependent on whether the Hund's coupling is full or of Ising type. The critical values and the nature of the OSM transitions are efficiently determined by entanglement entropy. We reveal that vanishing of the Kondo energy scale evidenced by absence of local spin fluctuations at low frequency in local dynamical spin susceptibility is responsible for the appearance of non-Fermi-liquid OSM phase in Ising Hund's coupling case. We argue that this scenario can also be applied to account for emergent quantum non-Fermi liquid in the one-band Hubbard model when short-range antiferromagnetic order is considered.

On discrete field theory properties of the dimer and Ising models and their conformal field theory limits

NASA Astrophysics Data System (ADS)

Kriz, Igor; Loebl, Martin; Somberg, Petr

2013-05-01

We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding conjectured limits realized by fermions in rational conformal field theories.

Coarsening and persistence in a one-dimensional system of orienting arrowheads: Domain-wall kinetics with A +B →0

NASA Astrophysics Data System (ADS)

Khandkar, Mahendra D.; Stinchcombe, Robin; Barma, Mustansir

2017-01-01

We demonstrate the large-scale effects of the interplay between shape and hard-core interactions in a system with left- and right-pointing arrowheads <> on a line, with reorientation dynamics. This interplay leads to the formation of two types of domain walls, >< (A ) and <> (B ). The correlation length in the equilibrium state diverges exponentially with increasing arrowhead density, with an ordered state of like orientations arising in the limit. In this high-density limit, the A domain walls diffuse, while the B walls are static. In time, the approach to the ordered state is described by a coarsening process governed by the kinetics of domain-wall annihilation A +B →0 , quite different from the A +A →0 kinetics pertinent to the Glauber-Ising model. The survival probability of a finite set of walls is shown to decay exponentially with time, in contrast to the power-law decay known for A +A →0 . In the thermodynamic limit with a finite density of walls, coarsening as a function of time t is studied by simulation. While the number of walls falls as t-1/2, the fraction of persistent arrowheads decays as t-θ where θ is close to 1/4 , quite different from the Ising value. The global persistence too has θ =1/4 , as follows from a heuristic argument. In a generalization where the B walls diffuse slowly, θ varies continuously, increasing with increasing diffusion constant.

Coarsening and persistence in a one-dimensional system of orienting arrowheads: Domain-wall kinetics with A+B→0.

PubMed

Khandkar, Mahendra D; Stinchcombe, Robin; Barma, Mustansir

2017-01-01

We demonstrate the large-scale effects of the interplay between shape and hard-core interactions in a system with left- and right-pointing arrowheads <> on a line, with reorientation dynamics. This interplay leads to the formation of two types of domain walls, >< (A) and <> (B). The correlation length in the equilibrium state diverges exponentially with increasing arrowhead density, with an ordered state of like orientations arising in the limit. In this high-density limit, the A domain walls diffuse, while the B walls are static. In time, the approach to the ordered state is described by a coarsening process governed by the kinetics of domain-wall annihilation A+B→0, quite different from the A+A→0 kinetics pertinent to the Glauber-Ising model. The survival probability of a finite set of walls is shown to decay exponentially with time, in contrast to the power-law decay known for A+A→0. In the thermodynamic limit with a finite density of walls, coarsening as a function of time t is studied by simulation. While the number of walls falls as t^{-1/2}, the fraction of persistent arrowheads decays as t^{-θ} where θ is close to 1/4, quite different from the Ising value. The global persistence too has θ=1/4, as follows from a heuristic argument. In a generalization where the B walls diffuse slowly, θ varies continuously, increasing with increasing diffusion constant.

Quantum gravity as an information network self-organization of a 4D universe

NASA Astrophysics Data System (ADS)

Trugenberger, Carlo A.

2015-10-01

I propose a quantum gravity model in which the fundamental degrees of freedom are information bits for both discrete space-time points and links connecting them. The Hamiltonian is a very simple network model consisting of a ferromagnetic Ising model for space-time vertices and an antiferromagnetic Ising model for the links. As a result of the frustration between these two terms, the ground state self-organizes as a new type of low-clustering graph with finite Hausdorff dimension 4. The spectral dimension is lower than the Hausdorff dimension: it coincides with the Hausdorff dimension 4 at a first quantum phase transition corresponding to an IR fixed point, while at a second quantum phase transition describing small scales space-time dissolves into disordered information bits. The large-scale dimension 4 of the universe is related to the upper critical dimension 4 of the Ising model. At finite temperatures the universe graph emerges without a big bang and without singularities from a ferromagnetic phase transition in which space-time itself forms out of a hot soup of information bits. When the temperature is lowered the universe graph unfolds and expands by lowering its connectivity, a mechanism I have called topological expansion. The model admits topological black hole excitations corresponding to graphs containing holes with no space-time inside and with "Schwarzschild-like" horizons with a lower spectral dimension.

Optimal structure and parameter learning of Ising models

DOE PAGES

Lokhov, Andrey; Vuffray, Marc Denis; Misra, Sidhant; ...

2018-03-16

Reconstruction of the structure and parameters of an Ising model from binary samples is a problem of practical importance in a variety of disciplines, ranging from statistical physics and computational biology to image processing and machine learning. The focus of the research community shifted toward developing universal reconstruction algorithms that are both computationally efficient and require the minimal amount of expensive data. Here, we introduce a new method, interaction screening, which accurately estimates model parameters using local optimization problems. The algorithm provably achieves perfect graph structure recovery with an information-theoretically optimal number of samples, notably in the low-temperature regime, whichmore » is known to be the hardest for learning. Here, the efficacy of interaction screening is assessed through extensive numerical tests on synthetic Ising models of various topologies with different types of interactions, as well as on real data produced by a D-Wave quantum computer. Finally, this study shows that the interaction screening method is an exact, tractable, and optimal technique that universally solves the inverse Ising problem.« less

Optimal structure and parameter learning of Ising models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lokhov, Andrey; Vuffray, Marc Denis; Misra, Sidhant

Reconstruction of the structure and parameters of an Ising model from binary samples is a problem of practical importance in a variety of disciplines, ranging from statistical physics and computational biology to image processing and machine learning. The focus of the research community shifted toward developing universal reconstruction algorithms that are both computationally efficient and require the minimal amount of expensive data. Here, we introduce a new method, interaction screening, which accurately estimates model parameters using local optimization problems. The algorithm provably achieves perfect graph structure recovery with an information-theoretically optimal number of samples, notably in the low-temperature regime, whichmore » is known to be the hardest for learning. Here, the efficacy of interaction screening is assessed through extensive numerical tests on synthetic Ising models of various topologies with different types of interactions, as well as on real data produced by a D-Wave quantum computer. Finally, this study shows that the interaction screening method is an exact, tractable, and optimal technique that universally solves the inverse Ising problem.« less

Magnetic properties of magnetic bilayer Kekulene structure: A Monte Carlo study

NASA Astrophysics Data System (ADS)

Jabar, A.; Masrour, R.

2018-06-01

In the present work, we have studied the magnetic properties of magnetic bilayer Kekulene structure with mixed spin-5/2 and spin-2 Ising model using Monte Carlo study. The magnetic phase diagrams of mixed spins Ising model have been given. The thermal total, partial magnetization and magnetic susceptibilities of the mixed spin-5/2 and spin-2 Ising model on a magnetic bilayer Kekulene structure are obtained. The transition temperature has been deduced. The effect of crystal field and exchange interactions on the this bilayers has been studied. The partial and total magnetic hysteresis cycles of the mixed spin-5/2 and spin-2 Ising model on a magnetic bilayer Kekulene structure have been given. The superparamagnetism behavior is observed in magnetic bilayer Kekulene structure. The magnetic coercive field decreases with increasing the exchange interactions between σ-σ and temperatures values and increases with increasing the absolute value of exchange interactions between σ-S. The multiple hysteresis behavior appears.

Fluxoids behavior in superconducting ladders

NASA Astrophysics Data System (ADS)

Sharon, Omri J.; Haham, Noam; Shaulov, Avner; Yeshurun, Yosef

2018-03-01

The nature of the interaction between fluxoids and between them and the external magnetic field is studied in one-dimensional superconducting networks. An Ising like expression is derived for the energy of a network revealing that fluxoids behave as repulsively interacting objects driven towards the network center by the effective applied field. Competition between these two interactions determines the equilibrium arrangement of fluxoids in the network as a function of the applied field. It is demonstrated that the fluxoids configurations are not always commensurate to the network symmetry. Incommensurate, degenerated configurations may be formed even in networks with an odd number of loops.

Visualization tool for three-dimensional plasma velocity distributions (ISEE_3D) as a plug-in for SPEDAS

NASA Astrophysics Data System (ADS)

Keika, Kunihiro; Miyoshi, Yoshizumi; Machida, Shinobu; Ieda, Akimasa; Seki, Kanako; Hori, Tomoaki; Miyashita, Yukinaga; Shoji, Masafumi; Shinohara, Iku; Angelopoulos, Vassilis; Lewis, Jim W.; Flores, Aaron

2017-12-01

This paper introduces ISEE_3D, an interactive visualization tool for three-dimensional plasma velocity distribution functions, developed by the Institute for Space-Earth Environmental Research, Nagoya University, Japan. The tool provides a variety of methods to visualize the distribution function of space plasma: scatter, volume, and isosurface modes. The tool also has a wide range of functions, such as displaying magnetic field vectors and two-dimensional slices of distributions to facilitate extensive analysis. The coordinate transformation to the magnetic field coordinates is also implemented in the tool. The source codes of the tool are written as scripts of a widely used data analysis software language, Interactive Data Language, which has been widespread in the field of space physics and solar physics. The current version of the tool can be used for data files of the plasma distribution function from the Geotail satellite mission, which are publicly accessible through the Data Archives and Transmission System of the Institute of Space and Astronautical Science (ISAS)/Japan Aerospace Exploration Agency (JAXA). The tool is also available in the Space Physics Environment Data Analysis Software to visualize plasma data from the Magnetospheric Multiscale and the Time History of Events and Macroscale Interactions during Substorms missions. The tool is planned to be applied to data from other missions, such as Arase (ERG) and Van Allen Probes after replacing or adding data loading plug-ins. This visualization tool helps scientists understand the dynamics of space plasma better, particularly in the regions where the magnetohydrodynamic approximation is not valid, for example, the Earth's inner magnetosphere, magnetopause, bow shock, and plasma sheet.

Quantum criticality of a spin-1 XY model with easy-plane single-ion anisotropy via a two-time Green function approach avoiding the Anderson-Callen decoupling

NASA Astrophysics Data System (ADS)

Mercaldo, M. T.; Rabuffo, I.; De Cesare, L.; Caramico D'Auria, A.

2016-04-01

In this work we study the quantum phase transition, the phase diagram and the quantum criticality induced by the easy-plane single-ion anisotropy in a d-dimensional quantum spin-1 XY model in absence of an external longitudinal magnetic field. We employ the two-time Green function method by avoiding the Anderson-Callen decoupling of spin operators at the same sites which is of doubtful accuracy. Following the original Devlin procedure we treat exactly the higher order single-site anisotropy Green functions and use Tyablikov-like decouplings for the exchange higher order ones. The related self-consistent equations appear suitable for an analysis of the thermodynamic properties at and around second order phase transition points. Remarkably, the equivalence between the microscopic spin model and the continuous O(2) -vector model with transverse-Ising model (TIM)-like dynamics, characterized by a dynamic critical exponent z=1, emerges at low temperatures close to the quantum critical point with the single-ion anisotropy parameter D as the non-thermal control parameter. The zero-temperature critic anisotropy parameter Dc is obtained for dimensionalities d > 1 as a function of the microscopic exchange coupling parameter and the related numerical data for different lattices are found to be in reasonable agreement with those obtained by means of alternative analytical and numerical methods. For d > 2, and in particular for d=3, we determine the finite-temperature critical line ending in the quantum critical point and the related TIM-like shift exponent, consistently with recent renormalization group predictions. The main crossover lines between different asymptotic regimes around the quantum critical point are also estimated providing a global phase diagram and a quantum criticality very similar to the conventional ones.

Internet Self-Efficacy Does Not Predict Student Use of Internet-Mediated Educational Technology

ERIC Educational Resources Information Center

Buchanan, Tom; Joban, Sanjay; Porter, Alan

2014-01-01

Two studies tested the hypothesis that use of learning technologies among undergraduate psychology students was associated with higher Internet self-efficacy (ISE). In Study 1, the ISE scores of 86 students were found not to be associated with either attitudes towards, or measured use of, blogs and wikis as part of an IT skills course. ISE was…

Characterizing quantum phase transition by teleportation

NASA Astrophysics Data System (ADS)

Wu, Meng-He; Ling, Yi; Shu, Fu-Wen; Gan, Wen-Cong

2018-04-01

In this paper we provide a novel way to explore the relation between quantum teleportation and quantum phase transition. We construct a quantum channel with a mixed state which is made from one dimensional quantum Ising chain with infinite length, and then consider the teleportation with the use of entangled Werner states as input qubits. The fidelity as a figure of merit to measure how well the quantum state is transferred is studied numerically. Remarkably we find the first-order derivative of the fidelity with respect to the parameter in quantum Ising chain exhibits a logarithmic divergence at the quantum critical point. The implications of this phenomenon and possible applications are also briefly discussed.

Casimir interaction of rodlike particles in a two-dimensional critical system.

PubMed

Eisenriegler, E; Burkhardt, T W

2016-09-01

We consider the fluctuation-induced interaction of two thin, rodlike particles, or "needles," immersed in a two-dimensional critical fluid of Ising symmetry right at the critical point. Conformally mapping the plane containing the needles onto a simpler geometry in which the stress tensor is known, we analyze the force and torque between needles of arbitrary length, separation, and orientation. For infinite and semi-infinite needles we utilize the mapping of the plane bounded by the needles onto the half plane, and for two needles of finite length we use the mapping onto an annulus. For semi-infinite and infinite needles the force is expressed in terms of elementary functions, and we also obtain analytical results for the force and torque between needles of finite length with separation much greater than their length. Evaluating formulas in our approach numerically for several needle geometries and surface universality classes, we study the full crossover from small to large values of the separation to length ratio. In these two limits the numerical results agree with results for infinitely long needles and with predictions of the small-particle operator expansion, respectively.

Monte Carlo simulation of Ising models by multispin coding on a vector computer

NASA Astrophysics Data System (ADS)

Wansleben, Stephan; Zabolitzky, John G.; Kalle, Claus

1984-11-01

Rebbi's efficient multispin coding algorithm for Ising models is combined with the use of the vector computer CDC Cyber 205. A speed of 21.2 million updates per second is reached. This is comparable to that obtained by special- purpose computers.

Anisotropic magnetic interactions and spin dynamics in the spin-chain compound Cu (py) 2Br2 : An experimental and theoretical study

NASA Astrophysics Data System (ADS)

Zeisner, J.; Brockmann, M.; Zimmermann, S.; Weiße, A.; Thede, M.; Ressouche, E.; Povarov, K. Yu.; Zheludev, A.; Klümper, A.; Büchner, B.; Kataev, V.; Göhmann, F.

2017-07-01

We compare theoretical results for electron spin resonance (ESR) properties of the Heisenberg-Ising Hamiltonian with ESR experiments on the quasi-one-dimensional magnet Cu (py) 2Br2 (CPB). Our measurements were performed over a wide frequency and temperature range giving insight into the spin dynamics, spin structure, and magnetic anisotropy of this compound. By analyzing the angular dependence of ESR parameters (resonance shift and linewidth) at room temperature, we show that the two weakly coupled inequivalent spin-chain types inside the compound are well described by Heisenberg-Ising chains with their magnetic anisotropy axes perpendicular to the chain direction and almost perpendicular to each other. We further determine the full g tensor from these data. In addition, the angular dependence of the linewidth at high temperatures gives us access to the exponent of the algebraic decay of a dynamical correlation function of the isotropic Heisenberg chain. From the temperature dependence of static susceptibilities, we extract the strength of the exchange coupling (J /kB=52.0 K ) and the anisotropy parameter (δ ≈-0.02 ) of the model Hamiltonian. An independent compatible value of δ is obtained by comparing the exact prediction for the resonance shift at low temperatures with high-frequency ESR data recorded at 4 K . The spin structure in the ordered state implied by the two (almost) perpendicular anisotropy axes is in accordance with the propagation vector determined from neutron scattering experiments. In addition to undoped samples, we study the impact of partial substitution of Br by Cl ions on spin dynamics. From the dependence of the ESR linewidth on the doping level, we infer an effective decoupling of the anisotropic component J δ from the isotropic exchange J in these systems.

Thermal properties of the mixed spin-1 and spin-3/2 Ising ferrimagnetic system with two different random single-ion anisotropies

NASA Astrophysics Data System (ADS)

Pereira, J. R. V.; Tunes, T. M.; de Arruda, A. S.; Godoy, M.

2018-06-01

In this work, we have performed Monte Carlo simulations to study a mixed spin-1 and spin-3/2 Ising ferrimagnetic system on a square lattice with two different random single-ion anisotropies. This lattice is divided in two interpenetrating sublattices with spins SA = 1 in the sublattice A and SB = 3 / 2 in the sublattice B. The exchange interaction between the spins on the sublattices is antiferromagnetic (J < 0). We used two random single-ion anisotropies, DiA and DjB , on the sublattices A and B, respectively. We have determined the phase diagram of the model in the critical temperature Tc versus strength of the random single-ion anisotropy D plane and we shown that it exhibits only second-order phase transition lines. We also shown that this system displays compensation temperatures for some cases of the random single-ion distribution.

Building a Science Software Institute: Synthesizing the Lessons Learned from the ISEES and WSSI Software Institute Conceptualization Efforts

NASA Astrophysics Data System (ADS)

Idaszak, R.; Lenhardt, W. C.; Jones, M. B.; Ahalt, S.; Schildhauer, M.; Hampton, S. E.

2014-12-01

The NSF, in an effort to support the creation of sustainable science software, funded 16 science software institute conceptualization efforts. The goal of these conceptualization efforts is to explore approaches to creating the institutional, sociological, and physical infrastructures to support sustainable science software. This paper will present the lessons learned from two of these conceptualization efforts, the Institute for Sustainable Earth and Environmental Software (ISEES - http://isees.nceas.ucsb.edu) and the Water Science Software Institute (WSSI - http://waters2i2.org). ISEES is a multi-partner effort led by National Center for Ecological Analysis and Synthesis (NCEAS). WSSI, also a multi-partner effort, is led by the Renaissance Computing Institute (RENCI). The two conceptualization efforts have been collaborating due to the complementarity of their approaches and given the potential synergies of their science focus. ISEES and WSSI have engaged in a number of activities to address the challenges of science software such as workshops, hackathons, and coding efforts. More recently, the two institutes have also collaborated on joint activities including training, proposals, and papers. In addition to presenting lessons learned, this paper will synthesize across the two efforts to project a unified vision for a science software institute.

Thermodynamic and critical properties of an antiferromagnetically stacked triangular Ising antiferromagnet in a field

NASA Astrophysics Data System (ADS)

Žukovič, M.; Borovský, M.; Bobák, A.

2018-05-01

We study a stacked triangular lattice Ising model with both intra- and inter-plane antiferromagnetic interactions in a field, by Monte Carlo simulation. We find only one phase transition from a paramagnetic to a partially disordered phase, which is of second order and 3D XY universality class. At low temperatures we identify two highly degenerate phases: at smaller (larger) fields the system shows long-range ordering in the stacking direction (within planes) but not in the planes (stacking direction). Nevertheless, crossovers to these phases do not have a character of conventional phase transitions but rather linear-chain-like excitations.

Three-dimensional magnetosheath plasma ion distributions from 200 eV to 2 MeV

NASA Technical Reports Server (NTRS)

Williams, D. J.; Mitchell, D. G.; Frank, L. A.; Eastman, T. E.

1988-01-01

This paper presents initial measurements, made with ISEE 1 plasma and energetic-particle instruments, of the three-dimensional magnetosheath plasma ion flow and the spectrum over the energy range of 200 eV to 2 MeV, obtained on two magnetosheath traversals, one on the dawn (December 19, 1977) and the other on the dusk (July 7, 1978) flanks of the magnetosphere. The data suggest that the magnetosheath plasma ion population often consisted of a shocked solar wind component, of energy not greater than 5 keV, and a magnetospheric high-energy (not below 5 keV) component. The shocked solar wind component generally behaved independently of the magnetic field direction, indicating that the magnetic field was carried along in the bulk plasma flow. The high-energy tail was highly modulated by the magnetic field.

Eigenpairs of Toeplitz and Disordered Toeplitz Matrices with a Fisher-Hartwig Symbol

NASA Astrophysics Data System (ADS)

Movassagh, Ramis; Kadanoff, Leo P.

2017-05-01

Toeplitz matrices have entries that are constant along diagonals. They model directed transport, are at the heart of correlation function calculations of the two-dimensional Ising model, and have applications in quantum information science. We derive their eigenvalues and eigenvectors when the symbol is singular Fisher-Hartwig. We then add diagonal disorder and study the resulting eigenpairs. We find that there is a "bulk" behavior that is well captured by second order perturbation theory of non-Hermitian matrices. The non-perturbative behavior is classified into two classes: Runaways type I leave the complex-valued spectrum and become completely real because of eigenvalue attraction. Runaways type II leave the bulk and move very rapidly in response to perturbations. These have high condition numbers and can be predicted. Localization of the eigenvectors are then quantified using entropies and inverse participation ratios. Eigenvectors corresponding to Runaways type II are most localized (i.e., super-exponential), whereas Runaways type I are less localized than the unperturbed counterparts and have most of their probability mass in the interior with algebraic decays. The results are corroborated by applying free probability theory and various other supporting numerical studies.

Critical behavior of the quasi-two-dimensional weak itinerant ferromagnet trigonal chromium telluride Cr 0.62 Te

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yu; Petrovic, C.

The critical properties of flux-grown single-crystalline quasi-two-dimensional weak itinerant ferromagnet Cr 0.62 Te were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic phase transition. Critical exponents β = 0.315 ( 7 ) with a critical temperature T c = 230.6 ( 3 ) K and γ = 1.81 ( 2 ) with T c = 229.1 ( 1 ) K are obtained by the Kouvel-Fisher method whereas δ = 6.35 ( 4 ) is obtained by a critical isotherm analysis at T c = 230 K. With these obtained exponents, the magnetization-field-temperature curves collapse into two independentmore » curves following a single scaling equation M | T-T c/T c| -β = f ± ( H |T-T c/T c| -β δ ) around T c , suggesting the reliability of the obtained exponents. Additionally, the determined exponents of Cr 0.62 Te exhibit an Ising-like behavior with a change from short-range order to long-range order in the nature of magnetic interaction and with an extension from two to three dimensions on cooling through T c.« less

Critical behavior of the quasi-two-dimensional weak itinerant ferromagnet trigonal chromium telluride Cr 0.62 Te

DOE PAGES

Liu, Yu; Petrovic, C.

2017-10-09

The critical properties of flux-grown single-crystalline quasi-two-dimensional weak itinerant ferromagnet Cr 0.62 Te were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic phase transition. Critical exponents β = 0.315 ( 7 ) with a critical temperature T c = 230.6 ( 3 ) K and γ = 1.81 ( 2 ) with T c = 229.1 ( 1 ) K are obtained by the Kouvel-Fisher method whereas δ = 6.35 ( 4 ) is obtained by a critical isotherm analysis at T c = 230 K. With these obtained exponents, the magnetization-field-temperature curves collapse into two independentmore » curves following a single scaling equation M | T-T c/T c| -β = f ± ( H |T-T c/T c| -β δ ) around T c , suggesting the reliability of the obtained exponents. Additionally, the determined exponents of Cr 0.62 Te exhibit an Ising-like behavior with a change from short-range order to long-range order in the nature of magnetic interaction and with an extension from two to three dimensions on cooling through T c.« less

Critical Behavior of the Annealed Ising Model on Random Regular Graphs

NASA Astrophysics Data System (ADS)

Can, Van Hao

2017-11-01

In Giardinà et al. (ALEA Lat Am J Probab Math Stat 13(1):121-161, 2016), the authors have defined an annealed Ising model on random graphs and proved limit theorems for the magnetization of this model on some random graphs including random 2-regular graphs. Then in Can (Annealed limit theorems for the Ising model on random regular graphs, arXiv:1701.08639, 2017), we generalized their results to the class of all random regular graphs. In this paper, we study the critical behavior of this model. In particular, we determine the critical exponents and prove a non standard limit theorem stating that the magnetization scaled by n^{3/4} converges to a specific random variable, with n the number of vertices of random regular graphs.

Lattice Supersymmetry and Order-Disorder Coexistence in the Tricritical Ising Model

NASA Astrophysics Data System (ADS)

O'Brien, Edward; Fendley, Paul

2018-05-01

We introduce and analyze a quantum spin or Majorana chain with a tricritical Ising point separating a critical phase from a gapped phase with order-disorder coexistence. We show that supersymmetry is not only an emergent property of the scaling limit but also manifests itself on the lattice. Namely, we find explicit lattice expressions for the supersymmetry generators and currents. Writing the Hamiltonian in terms of these generators allows us to find the ground states exactly at a frustration-free coupling. These confirm the coexistence between two (topologically) ordered ground states and a disordered one in the gapped phase. Deforming the model by including explicit chiral symmetry breaking, we find the phases persist up to an unusual chiral phase transition where the supersymmetry becomes exact even on the lattice.

Coevolution of Glauber-like Ising dynamics and topology

NASA Astrophysics Data System (ADS)

Mandrà, Salvatore; Fortunato, Santo; Castellano, Claudio

2009-11-01

We study the coevolution of a generalized Glauber dynamics for Ising spins with tunable threshold and of the graph topology where the dynamics takes place. This simple coevolution dynamics generates a rich phase diagram in the space of the two parameters of the model, the threshold and the rewiring probability. The diagram displays phase transitions of different types: spin ordering, percolation, and connectedness. At variance with traditional coevolution models, in which all spins of each connected component of the graph have equal value in the stationary state, we find that, for suitable choices of the parameters, the system may converge to a state in which spins of opposite sign coexist in the same component organized in compact clusters of like-signed spins. Mean field calculations enable one to estimate some features of the phase diagram.

Precision islands in the Ising and O(N ) models

DOE PAGES

Kos, Filip; Poland, David; Simmons-Duffin, David; ...

2016-08-04

We make precise determinations of the leading scaling dimensions and operator product expansion (OPE) coefficients in the 3d Ising, O(2), and O(3) models from the conformal bootstrap with mixed correlators. We improve on previous studies by scanning over possible relative values of the leading OPE coefficients, which incorporates the physical information that there is only a single operator at a given scaling dimension. The scaling dimensions and OPE coefficients obtained for the 3d Ising model, (Δ σ , Δ ϵ , λ σσϵ , λ ϵϵϵ ) = (0.5181489(10), 1.412625(10), 1.0518537(41), 1.532435(19) , give the most precise determinations of thesemore » quantities to date.« less

On the binding of calcium by micelles composed of carboxy-modified pluronics measured by means of differential potentiometric titration and modeled with a self-consistent-field theory.

PubMed

Lauw, Y; Leermakers, F A M; Cohen Stuart, M A; Pinheiro, J P; Custers, J P A; van den Broeke, L J P; Keurentjes, J T F

2006-12-19

We perform differential potentiometric titration measurements for the binding of Ca2+ ions to micelles composed of the carboxylic acid end-standing Pluronic P85 block copolymer (i.e., CAE-85 (COOH-(EO)26-(PO)39-(EO)26-COOH)). Two different ion-selective electrodes (ISEs) are used to detect the free calcium concentration; the first ISE is an indicator electrode, and the second is a reference electrode. The titration is done by adding the block copolymers to a known solution of Ca2+ at neutral pH and high enough temperature (above the critical micellization temperature CMT) and various amount of added monovalent salt. By measuring the difference in the electromotive force between the two ISEs, the amount of Ca2+ that is bound by the micelles is calculated. This is then used to determine the binding constant of Ca2+ with the micelles, which is a missing parameter needed to perform molecular realistic self-consistent-field (SCF) calculations. It turns out that the micelles from block copolymer CAE-85 bind Ca2+ ions both electrostatically and specifically. The specific binding between Ca2+ and carboxylic groups in the corona of the micelles is modeled through the reaction equilibrium -COOCa+ <==> -COO- + Ca2+ with pKCa = 1.7 +/- 0.06.

Orbital-selective Mott phases of a one-dimensional three-orbital Hubbard model studied using computational techniques

DOE PAGES

Liu, Guangkun; Kaushal, Nitin; Liu, Shaozhi; ...

2016-06-24

A recently introduced one-dimensional three-orbital Hubbard model displays orbital-selective Mott phases with exotic spin arrangements such as spin block states [J. Rincón et al., Phys. Rev. Lett. 112, 106405 (2014)]. In this paper we show that the constrained-path quantum Monte Carlo (CPQMC) technique can accurately reproduce the phase diagram of this multiorbital one-dimensional model, paving the way to future CPQMC studies in systems with more challenging geometries, such as ladders and planes. The success of this approach relies on using the Hartree-Fock technique to prepare the trial states needed in CPQMC. In addition, we study a simplified version of themore » model where the pair-hopping term is neglected and the Hund coupling is restricted to its Ising component. The corresponding phase diagrams are shown to be only mildly affected by the absence of these technically difficult-to-implement terms. This is confirmed by additional density matrix renormalization group and determinant quantum Monte Carlo calculations carried out for the same simplified model, with the latter displaying only mild fermion sign problems. Lastly, we conclude that these methods are able to capture quantitatively the rich physics of the several orbital-selective Mott phases (OSMP) displayed by this model, thus enabling computational studies of the OSMP regime in higher dimensions, beyond static or dynamic mean-field approximations.« less

Factors controlling degree of correlation between ISEE 1 and ISEE 3 interplanetary magnetic field measurements

NASA Technical Reports Server (NTRS)

Crooker, N. U.; Siscoe, G. L.; Russell, C. T.; Smith, E. J.

1982-01-01

Correlation variability between ISEE 1 and 3 IMF measurements is investigated, and factors governing the variability are discussed. About 200 two-hour periods when correlation was good, and 200 when correlation was poor, are examined, and both IMF variance and spacecraft separation distance in the plane perpendicular to the earth-sun line exert substantial control. The scale size of magnetic features is larger when variance is high, and abrupt changes in the correlation coefficient from poor to good or good to poor in adjacent two-hour intervals appear to be governed by the sense of change of IMF variance and vice versa. During periods of low variance, good correlations are most likely to occur when the distance between ISEE 1 and 3 perpendicular to the IMF is less than 20 earth radii.

Concurrence and fidelity of a Bose-Fermi mixture in a one-dimensional optical lattice.

PubMed

Ning, Wen-Qiang; Gu, Shi-Jian; Chen, Yu-Guang; Wu, Chang-Qin; Lin, Hai-Qing

2008-06-11

We study the ground-state fidelity and entanglement of a Bose-Fermi mixture loaded in a one-dimensional optical lattice. It is found that the fidelity is able to signal quantum phase transitions between the Luttinger liquid phase, the density-wave phase, and the phase separation state of the system, and the concurrence, as a measure of the entanglement, can be used to signal the transition between the density-wave phase and the Ising phase.

Exactly solved mixed spin-(1,1/2) Ising-Heisenberg diamond chain with a single-ion anisotropy

NASA Astrophysics Data System (ADS)

Lisnyi, Bohdan; Strečka, Jozef

2015-03-01

The mixed spin-(1,1/2) Ising-Heisenberg diamond chain with a single-ion anisotropy is exactly solved through the generalized decoration-iteration transformation and the transfer-matrix method. The decoration-iteration transformation is first used for establishing a rigorous mapping equivalence with the corresponding spin-1 Blume-Emery-Griffiths chain, which is subsequently exactly treated within the transfer-matrix technique. Apart from three classical ground states the model exhibits three striking quantum ground states in which a singlet-dimer state of the interstitial Heisenberg spins is accompanied either with a frustrated state or a polarized state or a non-magnetic state of the nodal Ising spins. It is evidenced that two magnetization plateaus at zero and/or one-half of the saturation magnetization may appear in low-temperature magnetization curves. The specific heat may display remarkable temperature dependences with up to three and four distinct round maxima in a zero and non-zero magnetic field, respectively.

Local non-Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice

NASA Astrophysics Data System (ADS)

Kim, Isaac H.

2011-05-01

We present a family of non-Calderbank-Shor-Steane quantum error-correcting code consisting of geometrically local stabilizer generators on a 3D lattice. We study the Hamiltonian constructed from ferromagnetic interaction of overcomplete set of local stabilizer generators. The degenerate ground state of the system is characterized by a quantum error-correcting code whose number of encoded qubits are equal to the second Betti number of the manifold. These models (i) have solely local interactions; (ii) admit a strong-weak duality relation with an Ising model on a dual lattice; (iii) have topological order in the ground state, some of which survive at finite temperature; and (iv) behave as classical memory at finite temperature.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stauffer, D.

After improving the Monte Carlo statistics, Derrida`s exponent {theta} for the never damaged sites in Ising models at finite temperatures is shown to be compatible with {theta}(T = 0) = 0.22 in two dimensions. In three and more dimensions the number of these sites decays differently from zero temperature

The third law of thermodynamics and the fractional entropies

NASA Astrophysics Data System (ADS)

Baris Bagci, G.

2016-08-01

We consider the fractal calculus based Ubriaco and Machado entropies and investigate whether they conform to the third law of thermodynamics. The Ubriaco entropy satisfies the third law of thermodynamics in the interval 0 < q ≤ 1 exactly where it is also thermodynamically stable. The Machado entropy, on the other hand, yields diverging inverse temperature in the region 0 < q ≤ 1, albeit with non-vanishing negative entropy values. Therefore, despite the divergent inverse temperature behavior, the Machado entropy fails the third law of thermodynamics. We also show that the aforementioned results are also supported by the one-dimensional Ising model with no external field.

Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model

NASA Astrophysics Data System (ADS)

Pan, Xue; Zhang, Yanhua; Chen, Lizhu; Xu, Mingmei; Wu, Yuanfang

2018-01-01

We study the sign distribution of generalized magnetic susceptibilities in the temperature-external magnetic field plane using the three-dimensional three-state Potts model. We find that the sign of odd-order susceptibility is opposite in the symmetric (disorder) and broken (order) phases, but that of the even-order one remains positive when it is far away from the phase boundary. When the critical point is approached from the crossover side, negative fourth-order magnetic susceptibility is observable. It is also demonstrated that non-monotonic behavior occurs in the temperature dependence of the generalized susceptibilities of the energy. The finite-size scaling behavior of the specific heat in this model is mainly controlled by the critical exponent of the magnetic susceptibility in the three-dimensional Ising universality class. Supported by Fund Project of National Natural Science Foundation of China (11647093, 11405088, 11521064), Fund Project of Sichuan Provincial Department of Education (16ZB0339), Fund Project of Chengdu Technological University (2016RC004) and the Major State Basic Research Development Program of China (2014CB845402)

Multifractality and Network Analysis of Phase Transition

PubMed Central

Li, Wei; Yang, Chunbin; Han, Jihui; Su, Zhu; Zou, Yijiang

2017-01-01

Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems. PMID:28107414

Tricriticality in the q-neighbor Ising model on a partially duplex clique.

PubMed

Chmiel, Anna; Sienkiewicz, Julian; Sznajd-Weron, Katarzyna

2017-12-01

We analyze a modified kinetic Ising model, a so-called q-neighbor Ising model, with Metropolis dynamics [Phys. Rev. E 92, 052105 (2015)PLEEE81539-375510.1103/PhysRevE.92.052105] on a duplex clique and a partially duplex clique. In the q-neighbor Ising model each spin interacts only with q spins randomly chosen from its whole neighborhood. In the case of a duplex clique the change of a spin is allowed only if both levels simultaneously induce this change. Due to the mean-field-like nature of the model we are able to derive the analytic form of transition probabilities and solve the corresponding master equation. The existence of the second level changes dramatically the character of the phase transition. In the case of the monoplex clique, the q-neighbor Ising model exhibits a continuous phase transition for q=3, discontinuous phase transition for q≥4, and for q=1 and q=2 the phase transition is not observed. On the other hand, in the case of the duplex clique continuous phase transitions are observed for all values of q, even for q=1 and q=2. Subsequently we introduce a partially duplex clique, parametrized by r∈[0,1], which allows us to tune the network from monoplex (r=0) to duplex (r=1). Such a generalized topology, in which a fraction r of all nodes appear on both levels, allows us to obtain the critical value of r=r^{*}(q) at which a tricriticality (switch from continuous to discontinuous phase transition) appears.

Static and Dynamic Properties of Ferroelectric Thin Film Memories.

NASA Astrophysics Data System (ADS)

Duiker, Hendrik Matthew

Several properties of ferroelectric thin-film memories have been modeled. First, it has been observed experimentally that the bulk phase KNO_3 has a first-order phase transition, and that the transition temperature of KNO_3 thin-films increases as the thickness of the film is decreased. A Landau theory of first-order phase transitions in bulk systems has been generalized by adding surface terms to the free energy expansion to account for these transition properties. The model successfully describes the observed transition properties and predicts the existence of films in which the surfaces are ordered at temperatures higher than the bulk transition temperature. Second, the Avrami model of polarization-reversal kinetics has been modified to describe the following cases: ferroelectrics composed of a large number of small grains; ferroelectric thin-films in which nucleation occurs at the surfaces, not in the bulk; ferroelectrics in which long-range dipolar interactions significantly affect the nucleation rate; and non-square wave switching pulses. The models were verified by applying them to the results of two-dimensional Ising model simulations. It was shown that the models allow the possibility of directly obtaining microscopic parameters, such as the nucleation rate and domain wall velocity, from bulk measurements. Finally, a model describing the fatigue of ferroelectric memories has been developed. As a ferroelectric memory fatigues the spontaneous polarization per unit volume decreases, the switching time decreases, and eventually the memory "shorts out" and becomes conducting. The model assumes the following: during each polarization reversal the film undergoes, every unit cell in the film has a chance of "degrading" and thus losing an ion. Degraded cells no longer contribute to the polarization. The ions are allowed to diffuse to the surfaces of the film and form, with other ions, conducting dendrites which grow into the bulk of the film. Computer simulations performed on a two dimensional lattice with the above model successfully described the phenomena observed during the fatigue of PZT and other types of ferroelectric thin-film memories films.

Magnetic phase diagram, static properties and relaxation of the insulating spin glass Co 1- xMn x(SCN) 2(CH 3OH) 2

NASA Astrophysics Data System (ADS)

DeFotis, G. C.; Just, E. M.; Pugh, V. J.; Coffey, G. A.; Hogg, B. D.; Fitzhenry, S. L.; Marmorino, J. L.; Krovich, D. J.; Chamberlain, R. V.

1999-07-01

The magnetic behavior of Co 1- xMn x(SCN) 2(CH 3OH) 2 has been studied by DC magnetization and susceptibility measurements on mixtures spanning the complete composition range. The pure components are a quasi-two-dimensional Heisenberg antiferromagnet (Mn system) and a three-dimensional Ising antiferromagnet (Co system). The crystal structure of the cobalt constituent is determined, and is closely related to that of the manganese constituent. Competing orthogonal spin anisotropies should occur in mixtures, and frustration effects arising from competing ferromagnetic and antiferromagnetic interactions may also arise. The Curie and Weiss constants, in χM= C/( T- θ), vary regularly with composition. C versus x is essentially linear while θ versus x shows a definite curvature, analysis of which reveals that the unlike-ion exchange interaction is antiferromagnetic and stronger than the like-ion interactions. The magnetic susceptibility is field dependent, more markedly so with increasing x. Plots of M/ H versus T exhibit maxima at low temperatures only for mixtures substantially richer in cobalt than manganese. Magnetic transition temperatures are estimated from these data. Magnetization versus field isotherms evolve with composition and with temperature; those for x=0.24 5 and 0.16 9 exhibit S-shapes for temperatures at or below the identified transitions. The nonlinear susceptibility versus temperature for x=0.24 5 displays structure but does not diverge. The temperature dependence of the thermoremanent magnetization (TRM) for x=0.24 5 shows characteristic features but does not follow any simple form. The time-dependence of the TRM is fitted at a series of temperatures employing a stretched exponential decay form. The thermal variation of the fit parameters is systematic and suggests that temperatures just below 3 K and slightly above 6 K have special significance. Over a limited temperature range the TRM is found to scale approximately as T log10(t/τ 0) , with τ0≈10 -12 s. Strong and weak irreversibility lines are determined for x=0.24 5; both vary as τg∝ h0.56, with zero-field temperatures of Ts(0)=5.5 5 K and Tw(0)=9.8 5 K, respectively. The exponent is closer to that recently predicted (0.53) for a short-range three-dimensional Ising spin glass than to the value 2/3 of the DeAlmeida-Thouless line in the infinite range mean-field Ising model. The existence of strong random anisotropy may account for the presence of a weak irreversibility line with the observed exponent. The T- x magnetic phase diagram exhibits a crossing of paramagnetic-ordered state phase boundaries and an associated tetracritical point at x≈0.20 5 and T≈2.6 0 K. Spin glass properties are apparent for compositions close to the tetracritical point.

Effects of quantum coherence on work statistics

NASA Astrophysics Data System (ADS)

Xu, Bao-Ming; Zou, Jian; Guo, Li-Sha; Kong, Xiang-Mu

2018-05-01

In the conventional two-point measurement scheme of quantum thermodynamics, quantum coherence is destroyed by the first measurement. But as we know the coherence really plays an important role in the quantum thermodynamics process, and how to describe the work statistics for a quantum coherent process is still an open question. In this paper, we use the full counting statistics method to investigate the effects of quantum coherence on work statistics. First, we give a general discussion and show that for a quantum coherent process, work statistics is very different from that of the two-point measurement scheme, specifically the average work is increased or decreased and the work fluctuation can be decreased by quantum coherence, which strongly depends on the relative phase, the energy level structure, and the external protocol. Then, we concretely consider a quenched one-dimensional transverse Ising model and show that quantum coherence has a more significant influence on work statistics in the ferromagnetism regime compared with that in the paramagnetism regime, so that due to the presence of quantum coherence the work statistics can exhibit the critical phenomenon even at high temperature.

[Direct and indirect ion selective electrodes methods: the differences specified through a case of Waldenström's macroglobulinemia].

PubMed

Zelmat, Mohamed Sofiane

2015-01-01

Direct and indirect ion selective electrodes (ISEs) are two methods commonly used in biochemistry laboratories in order to measure the electrolytes such as sodium. In the clinical practice, it's the sodium concentration in plasma water -measured by direct ISE- which is important to consider as it is responsible of water movements between the liquid compartments. Knowing the difference between the two methods is important because there are situations leading to conflicting results between direct and indirect ISE, especially with sodium and inappropriate therapeutic decisions could be taken if the clinician is not aware of this difference. The increase and the decrease in plasma water volume are the situations that distort the results of the indirect ISE because this method, after a dilution step, does not take into account the real percentage of plasma water of the patient in the determination of the concentrations (leading for sodium to pseudohyponatremia, pseudonormonatremia or pseudohypernatremia). In the direct ISE, the sample is not diluted and the results are correct even if the volume of plasma water is modified. This article specifies the differences between the two techniques through a case of Waldenström's macroglobulinemia and proposes a course of action to follow for both of the biologist and the clinician.

Ising model versus normal form game

NASA Astrophysics Data System (ADS)

Galam, Serge; Walliser, Bernard

2010-02-01

The 2-spin Ising model in statistical mechanics and the 2×2 normal form game in game theory are compared. All configurations allowed by the second are recovered by the first when the only concern is about Nash equilibria. But it holds no longer when Pareto optimum considerations are introduced as in the prisoner’s dilemma. This gap can nevertheless be filled by adding a new coupling term to the Ising model, even if that term has up to now no physical meaning. An individual complete bilinear objective function is thus found to be sufficient to reproduce all possible configurations of a 2×2 game. Using this one-to-one mapping new perspectives for future research in both fields can be envisioned.

Finite T spectral function of a single carrier injected into an Ising chain: a comparison of 3 different models

NASA Astrophysics Data System (ADS)

Moeller, Mirko; Berciu, Mona

2015-03-01

When studying the properties of complex, magnetic materials it is often necessary to work with effective Hamiltonians. In many cases the effective Hamiltonian is obtained by mapping the full, multiband Hamiltonian onto a simpler, single band model. A prominent example is the use of Zhang-Rice singlets to map the multiband Emery model for cuprates onto the single band t - J -model. Such mappings are usually done at zero temperature (T) and it is implicitly assumed that they are justified at finite T, as well. We present results on 3 different models of a single charge carrier (electron or hole) injected into a ferromagnetic Ising chain. Model I is a two band, two sublattice model, Model II is a two band, single sublattice model, and Model III is a single band model, the so called t -Jz -model. Due to the absence of spin-flip terms, a numerically exact solution of all 3 Models is possible, even at finite T. At zero T a mapping between all 3 models results in the same low energy physics. However, this is no longer true at finite T. Here the low energy behavior of Model III is significantly different from that of Models I and II. The reasons for this discrepancy and its implications for more realistic models (higher dimension, inclusion of spin-flip terms) are discussed. This work was supported by NSERC, QMI and the UBC 4YF (M.M.).

An analysis of intergroup rivalry using Ising model and reinforcement learning

NASA Astrophysics Data System (ADS)

Zhao, Feng-Fei; Qin, Zheng; Shao, Zhuo

2014-01-01

Modeling of intergroup rivalry can help us better understand economic competitions, political elections and other similar activities. The result of intergroup rivalry depends on the co-evolution of individual behavior within one group and the impact from the rival group. In this paper, we model the rivalry behavior using Ising model. Different from other simulation studies using Ising model, the evolution rules of each individual in our model are not static, but have the ability to learn from historical experience using reinforcement learning technique, which makes the simulation more close to real human behavior. We studied the phase transition in intergroup rivalry and focused on the impact of the degree of social freedom, the personality of group members and the social experience of individuals. The results of computer simulation show that a society with a low degree of social freedom and highly educated, experienced individuals is more likely to be one-sided in intergroup rivalry.

Dielectric properties of calicum and barium-doped strontium titanate

NASA Astrophysics Data System (ADS)

Tung, Li-Chun

Dielectric properties of high quality polycrystalline Ca- and Ba-doped SrTiO3 perovskites are studied by means of dielectric constant, dielectric loss and ferroelectric hysteresis measurements. Low frequency dispersion of the dielectric constant is found to be very small and a simple relaxor model may not be able to explain its dielectric behavior. Relaxation modes are found in these samples, and they are all interpreted as thermally activated Bipolar re-orientation across energy barriers. In Sr1- xCaxTiO3 (x = 0--0.3), two modes are found associated with different relaxation processes, and the concentration dependence implies a competition between these processes. In Sr1-xBa xTiO3 (x = 0--0.25), relaxation modes are found to be related to the structural transitions, and the relaxation modes persist at low doping levels (x < 0.1), where structural ordering is not observed by previous neutron scattering studies. The validity of well-accepted Barret formula is discussed and two of the well-accepted models, anharmonic oscillator model and transverse Ising model, are found to be equivalent. Both of the Ca and Ba systems can be understood qualitatively within the concept of transverse Ising model.

Exact phase boundaries and topological phase transitions of the X Y Z spin chain

NASA Astrophysics Data System (ADS)

Jafari, S. A.

2017-07-01

Within the block spin renormalization group, we give a very simple derivation of the exact phase boundaries of the X Y Z spin chain. First, we identify the Ising order along x ̂ or y ̂ as attractive renormalization group fixed points of the Kitaev chain. Then, in a global phase space composed of the anisotropy λ of the X Y interaction and the coupling Δ of the Δ σzσz interaction, we find that the above fixed points remain attractive in the two-dimesional parameter space. We therefore classify the gapped phases of the X Y Z spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain, which in turn is characterized by winding number ±1 , depending on whether the Ising order parameter is along x ̂ or y ̂ directions; or (2) attracted to the charge density wave (CDW) phases of the underlying Jordan-Wigner fermions, which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the X Y Z model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the X Y Z model justifies why our analytical solution of the three-site problem that is at the core of the present renormalization group treatment is able to produce the exact phase boundaries of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the CDW-Ising phase is entitled to host appropriate form of zero modes. We further observe that in the Kitaev-chain the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.

Magnetization switching in nanoscale ferromagnetic grains: MFM observables from Monte Carlo simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Richards, H.L.; Sides, S.W.; Novotny, M.A.

1996-12-31

Recently experimental techniques, such as magnetic force microscopy (MFM), have enabled the magnetic state of individual sub-micron particles to be resolved. Motivated by these experimental developments, the authors use Monte Carlo simulations of two-dimensional kinetic Ising ferromagnets to study the magnetic relaxation in a negative applied field of a grain with an initial magnetization m{sub 0} = + 1. They use classical droplet theory to predict the functional forms for some quantities which can be observed by MFM. An example is the probability that the magnetization is positive, which is a function of time, field, grain size, and grain dimensionality.more » The qualitative agreement between experiments and their simulations of switching in individual single-domain ferromagnets indicates that the switching mechanism in such particles may involve local nucleation and subsequent growth of droplets of the stable phase.« less

Entanglement entropy for the long-range Ising chain in a transverse field.

PubMed

Koffel, Thomas; Lewenstein, M; Tagliacozzo, Luca

2012-12-28

We consider the Ising model in a transverse field with long-range antiferromagnetic interactions that decay as a power law with their distance. We study both the phase diagram and the entanglement properties as a function of the exponent of the interaction. The phase diagram can be used as a guide for future experiments with trapped ions. We find two gapped phases, one dominated by the transverse field, exhibiting quasi-long-range order, and one dominated by the long-range interaction, with long-range Néel ordered ground states. We determine the location of the quantum critical points separating those two phases. We determine their critical exponents and central charges. In the phase with quasi-long-range order the ground states exhibit exotic corrections to the area law for the entanglement entropy coexisting with gapped entanglement spectra.

On the ground-state degeneracy and entropy in a double-tetrahedral chain formed by the localized Ising spins and mobile electrons

NASA Astrophysics Data System (ADS)

Gálisová, Lucia

2018-05-01

Ground-state properties of a hybrid double-tetrahedral chain, in which the localized Ising spins regularly alternate with triangular plaquettes occupied by a variable number of mobile electrons, are exactly investigated. We demonstrate that the zero-temperature phase diagram of the model involves several non-degenerate, two-fold degenerate and macroscopically degenerate chiral phases. Low-temperature dependencies of the entropy and specific heat are also examined in order to gain a deeper insight into the degeneracy of individual ground-state phases and phase transitions. It is shown that a diversity of the ground-state degeneracy manifests itself in multiple-peak structures of both thermodynamic quantities. A remarkable temperature dependencies of the specific heat with two and three Schottky-type maxima are discussed in detail.

Stability of the quantum Sherrington-Kirkpatrick spin glass model

NASA Astrophysics Data System (ADS)

Young, A. P.

2017-09-01

I study in detail the quantum Sherrington-Kirkpatrick (SK) model, i.e., the infinite-range Ising spin glass in a transverse field, by solving numerically the effective one-dimensional model that the quantum SK model can be mapped to in the thermodynamic limit. I find that the replica symmetric solution is unstable down to zero temperature, in contrast to some previous claims, and so there is not only a line of transitions in the (longitudinal) field-temperature plane (the de Almeida-Thouless, AT, line) where replica symmetry is broken, but also a quantum de Almeida-Thouless (QuAT) line in the transverse field-longitudinal field plane at T =0 . If the QuAT line also occurs in models with short-range interactions its presence might affect the performance of quantum annealers when solving spin glass-type problems with a bias (i.e., magnetic field).

Neutron diffraction study of antiferromagnetic ErNi3Ga9 in magnetic fields

NASA Astrophysics Data System (ADS)

Ninomiya, Hiroki; Sato, Takaaki; Matsumoto, Yuji; Moyoshi, Taketo; Nakao, Akiko; Ohishi, Kazuki; Kousaka, Yusuke; Akimitsu, Jun; Inoue, Katsuya; Ohara, Shigeo

2018-05-01

We report specific heat, magnetization, magnetoresistance, and neutron diffraction measurements of single crystals of ErNi3Ga9. This compound crystalizes in a chiral structure with space group R 32 . The erbium ions form a two-dimensional honeycomb structure. ErNi3Ga9 displays antiferromagnetic order below 6.4 K. We determined that the magnetic structure is slightly amplitude-modulated as well as antiferromagnetic with q = (0 , 0 , 0.5) . The magnetic properties are described by an Ising-like model in which the magnetic moment is always along the c-axis owing to the large uniaxial anisotropy caused by the crystalline electric field effect in the low temperature region. When the magnetic field is applied along the c-axis, a metamagnetic transition is observed around 12 kOe at 2 K. ErNi3Ga9 possesses crystal chirality, but the antisymmetric magnetic interaction, the so-called Dzyaloshinskii-Moriya (DM) interaction, does not contribute to the magnetic structure, because the magnetic moments are parallel to the DM-vector.

Floquet Symmetry-Protected Topological Phases in Cold-Atom Systems

NASA Astrophysics Data System (ADS)

Potirniche, I.-D.; Potter, A. C.; Schleier-Smith, M.; Vishwanath, A.; Yao, N. Y.

2017-09-01

We propose and analyze two distinct routes toward realizing interacting symmetry-protected topological (SPT) phases via periodic driving. First, we demonstrate that a driven transverse-field Ising model can be used to engineer complex interactions which enable the emulation of an equilibrium SPT phase. This phase remains stable only within a parametric time scale controlled by the driving frequency, beyond which its topological features break down. To overcome this issue, we consider an alternate route based upon realizing an intrinsically Floquet SPT phase that does not have any equilibrium analog. In both cases, we show that disorder, leading to many-body localization, prevents runaway heating and enables the observation of coherent quantum dynamics at high energy densities. Furthermore, we clarify the distinction between the equilibrium and Floquet SPT phases by identifying a unique micromotion-based entanglement spectrum signature of the latter. Finally, we propose a unifying implementation in a one-dimensional chain of Rydberg-dressed atoms and show that protected edge modes are observable on realistic experimental time scales.

The UCSD Time-dependent Tomography and IPS use for Exploring Space Weather Events

NASA Astrophysics Data System (ADS)

Yu, H. S.; Jackson, B. V.; Buffington, A.; Hick, P. P.; Tokumaru, M.; Odstrcil, D.; Kim, J.; Yun, J.

2016-12-01

The University of California, San Diego (UCSD) time-dependent, iterative, kinematic reconstruction technique has been used and expanded upon for over two decades. It provides some of the most-accurate predictions and three-dimensional (3D) analyses of heliospheric solar-wind parameters now available using interplanetary scintillation (IPS) data. The parameters provided include reconstructions of velocity, density, and three-component magnetic fields. Precise time-dependent results are now obtained at any solar distance in the inner heliosphere using ISEE (formerly STELab), Japan, IPS data sets, and can be used to drive 3D-MHD models including ENLIL. Using IPS data, these reconstructions provide a real-time prediction of the global solar wind parameters across the whole heliosphere with a time cadence of about one day (see http://ips.ucsd.edu). Here we compare the results (such as density, velocity, and magnetic fields) from the IPS tomography with different in-situ measurements and discuss several specific space weather events that demonstrate the issues resulting from these analyses.

Dynamical quantum phase transitions in extended transverse Ising models

NASA Astrophysics Data System (ADS)

Bhattacharjee, Sourav; Dutta, Amit

2018-04-01

We study the dynamical quantum phase transitions (DQPTs) manifested in the subsequent unitary dynamics of an extended Ising model with an additional three spin interactions following a sudden quench. Revisiting the equilibrium phase diagram of the model, where different quantum phases are characterized by different winding numbers, we show that in some situations the winding number may not change across a gap closing point in the energy spectrum. Although, usually there exists a one-to-one correspondence between the change in winding number and the number of critical time scales associated with DQPTs, we show that the extended nature of interactions may lead to unusual situations. Importantly, we show that in the limit of the cluster Ising model, three critical modes associated with DQPTs become degenerate, thereby leading to a single critical time scale for a given sector of Fisher zeros.

Influence of sad mood induction on implicit self-esteem and its relationship with symptoms of depression and anxiety.

PubMed

van Tuijl, Lonneke A; Verwoerd, Johan R L; de Jong, Peter J

2018-02-13

Implicit self-esteem (ISE) refers to the valence of triggered associations when the self is activated. Despite theories, previous studies often fail to observe low ISE in depression and anxiety. It is feasible that sad mood is required to activate dysfunctional self-associations. The present study tested the following hypotheses: i) ISE is lower following a sad mood induction (SMI); ii) the relationship between ISE and level of depression/anxiety symptoms is relatively strong when ISE is measured during sad mood; iii) individuals with higher levels of depression/anxiety symptoms will show a relatively large decrease in ISE following a SMI. In this mixed-designed study, university students completed the self-esteem implicit association test (IAT) either at baseline (control condition; n = 46) or following a SMI (experimental condition; n = 49). To test the third hypothesis, a SMI and IAT were also given in the control condition. Both conditions completed self-report measures of explicit self-esteem (ESE), and symptoms of depression and anxiety. There was no support for the first two hypotheses, but some support that symptoms of anxiety correlated with larger decreases in ISE following a SMI which partly supported the third hypothesis. This disappeared when controlling for multiple testing. Results are limited to non-clinical participants. While ISE was robust against increases in sad mood, there was some tentative support that symptoms of anxiety were related to larger decreases in ISE following a SMI. Copyright © 2018. Published by Elsevier Ltd.

A flower-like Ising model. Thermodynamic properties

NASA Astrophysics Data System (ADS)

Mejdani, R.; Ifti, M.

1995-03-01

We consider a flower-like Ising model, in which there are some additional bonds (in the “flower-core”) compared to a pure Ising chain. To understand the behaviour of this system and particularly the competition between ferromagnetic (usual) bonds along the chain and antiferromagnetic (additional) bonds across the chain, we study analytically and iteratively the main thermodynamic quantities. Very interesting is, in the zero-field and zero-temperature limit, the behaviour of the magnetization and the susceptibility, closely related to the ground state configurations and their degeneracies. This degeneracy explains the existence of non-zero entropy at zero temperature, in our results. Also, this model could be useful for the experimental investigations in studying the saturation curves for the enzyme kinetics or the melting curves for DNA-denaturation in some flower-like configurations.

Nonlinear spin susceptibility in topological insulators

NASA Astrophysics Data System (ADS)

Shiranzaei, Mahroo; Fransson, Jonas; Cheraghchi, Hosein; Parhizgar, Fariborz

2018-05-01

We revise the theory of the indirect exchange interaction between magnetic impurities beyond the linear response theory to establish the effect of impurity resonances in the surface states of a three-dimensional topological insulator. The interaction is composed of isotropic Heisenberg, anisotropic Ising, and Dzyaloshinskii-Moriya types of couplings. We find that all three contributions are finite at the Dirac point, which is in stark contrast to the linear response theory which predicts a vanishing Dzyaloshinskii-Moriya-type contribution. We show that the spin-independent component of the impurity scattering can generate large values of the Dzyaloshinskii-Moriya-type coupling in comparison with the Heisenberg and Ising types of couplings, while these latter contributions drastically reduce in magnitude and undergo sign changes. As a result, both collinear and noncollinear configurations are allowed magnetic configurations of the impurities.

Evidence for single-chain magnet behavior in a Mn(III)-Ni(II) chain designed with high spin magnetic units: a route to high temperature metastable magnets.

PubMed

Clérac, Rodolphe; Miyasaka, Hitoshi; Yamashita, Masahiro; Coulon, Claude

2002-10-30

We herein present the synthesis, crystal structure, and magnetic properties of a new heterometallic chain of MnIII and NiII ions, [Mn2(saltmen)2Ni(pao)2(py)2](ClO4)2 (1) (saltmen2- = N,N'-(1,1,2,2-tetramethylethylene) bis(salicylideneiminate) and pao- = pyridine-2-aldoximate). The crystal structure of 1 was investigated by X-ray crystallographic analysis: compound 1 crystallized in monoclinic, space group C2/c (No. 15) with a = 21.140(3) A, b = 15.975(1) A, c = 18.6212(4) A, beta = 98.0586(4) degrees , V = 6226.5(7) A3, and Z = 4. This compound consists of two fragments, the out-of-plane dimer [Mn2(saltmen)2]2+ as a coordination acceptor building block and the neutral mononuclear unit [Ni(pao)2(py)2] as a coordination donor building block, forming an alternating chain having the repeating unit [-Mn-(O)2-Mn-ON-Ni-NO-]n. In the crystal structure, each chain is well separated with a minimum intermetallic distance between Mn and Ni ions of 10.39 A and with the absence of interchain pi overlaps between organic ligands. These features ensure a good magnetic isolation of the chains. The dc and ac magnetic measurements were performed on both the polycrystalline sample and the aligned single crystals of 1. Above 30 K, the magnetic susceptibility of this one-dimensional compound was successfully described in a mean field approximation as an assembly of trimers (Mn...Ni...Mn) with a NiII...MnIII antiferromagnetic interaction (J = -21 K) connected through a ferromagnetic MnIII...MnIII interaction (J'). However, the mean field theory fails to describe the magnetic behavior below 30 K emphasizing the one-dimensional magnetic character of the title compound. Between 5 and 15 K, the susceptibility in the chain direction was fitted to a one-dimensional Ising model leading to the same value of J'. Hysteresis loops are observed below 3.5 K, indicating a magnet-type behavior. In the same range of temperature, combined ac and dc measurements show a slow relaxation of the magnetization. This result indicates the presence of a metastable state without magnetic long-range order. This material is the first experimental design of a heterometallic chain with ST = 3 magnetic units showing a "single-chain magnet" behavior predicted in 1963 by R. J. Glauber for an Ising one-dimensional system. This work opens new perspectives for one-dimensional systems to obtain high temperature metastable magnets by combining high spin magnetic units, strong interunit interactions, and uniaxial anisotropy.

Institute for Science and Engineering Simulation (ISES)

DTIC Science & Technology

2015-12-18

performance and other functionalities such as electrical , magnetic, optical, thermal, biological, chemical, and so forth. Structural integrity...transmission electron microscopy (HRSTEM) and three-dimensional atom probe (3DAP) tomography , the true atomic scale structure and change in chemical...atom probe tomography (3DAP) techniques, has permitted characterizing and quantifying the multimodal size distribution of different generations of γ

Nanothermodynamics Applied to Thermal Processes in Heterogeneous Materials

DTIC Science & Technology

2012-08-03

models agree favorably with a wide range of measurements of local thermal and dynamic properties. Progress in understanding basic thermodynamic...Monte- Carlo (MC) simulations of the Ising model .7 The solid black lines in Fig. 4 show results using the uncorrected (Metropolis) algorithm on the...parameter g=0.5 (green, dash-dot), g=1 (black, solid ), and g=2 (blue, dash-dot-dot). Note the failure of the standard Ising model (g=0) to match

Indentation size effects in single crystal copper as revealed by synchrotron x-ray microdiffraction

NASA Astrophysics Data System (ADS)

Feng, G.; Budiman, A. S.; Nix, W. D.; Tamura, N.; Patel, J. R.

2008-08-01

For a Cu single crystal, we find that indentation hardness increases with decreasing indentation depth, a phenomenon widely observed before and called the indentation size effect (ISE). To understand the underlying mechanism, we measure the lattice rotations in indentations of different sizes using white beam x-ray microdiffraction (μXRD); the indentation-induced lattice rotations are directly measured by the streaking of x-ray Laue spots associated with the indentations. The magnitude of the lattice rotations is found to be independent of indentation size, which is consistent with the basic tenets of the ISE model. Using the μXRD data together with an ISE model, we can estimate the effective radius of the indentation plastic zone, and the estimate is consistent with the value predicted by a finite element analysis. Using these results, an estimate of the average dislocation densities within the plastic zones has been made; the findings are consistent with the ISE arising from a dependence of the dislocation density on the depth of indentation.

Performance evaluation of coherent Ising machines against classical neural networks

NASA Astrophysics Data System (ADS)

Haribara, Yoshitaka; Ishikawa, Hitoshi; Utsunomiya, Shoko; Aihara, Kazuyuki; Yamamoto, Yoshihisa

2017-12-01

The coherent Ising machine is expected to find a near-optimal solution in various combinatorial optimization problems, which has been experimentally confirmed with optical parametric oscillators and a field programmable gate array circuit. The similar mathematical models were proposed three decades ago by Hopfield et al in the context of classical neural networks. In this article, we compare the computational performance of both models.

Tsunami Waves and Tsunami-Induced Natural Oscillations Determined by HF Radar in Ise Bay, Japan

NASA Astrophysics Data System (ADS)

Toguchi, Y.; Fujii, S.; Hinata, H.

2018-04-01

Tsunami waves and the subsequent natural oscillations generated by the 2011 Tohoku earthquake were observed by two high-frequency (HF) radars and four tidal gauge records in Ise Bay. The radial velocity components of both records increased abruptly at approximately 17:00 (JST) and continued for more than 24 h. This indicated that natural oscillations followed the tsunami in Ise Bay. The spectral analyses showed that the tsunami wave arrivals had periods of 16-19, 30-40, 60-90, and 120-140 min. The three longest periods were remarkably amplified. Time-frequency analysis also showed the energy increase and duration of these periods. We used an Empirical Orthogonal Function (EOF) to analyze the total velocity of the currents to find the underlying oscillation patterns in the three longest periods. To verify the physical properties of the EOF analysis results, we calculated the oscillation modes in Ise Bay using a numerical model proposed by Loomis. The results of EOF analysis showed that the oscillation modes of 120-140 and 60-90 min period bands were distributed widely, whereas the oscillation mode of the 30-40 min period band was distributed locally. The EOF spatial patterns of each period showed good agreement with the eigenmodes calculated by the method of Loomis (1975). Thus, the HF radars were capable of observing the tsunami arrival and the subsequent oscillations.

Ising Model on Tangled Chain, Some Thermodynamic Properties

NASA Astrophysics Data System (ADS)

Mejdani, R.

1996-09-01

In this paper we consider an Ising model on tangled chain, where some additional bonds compared to a pure Ising chain are presented. To understand the behavior of this system and the competition between ferromagnetic bonds J along the chain and antiferromagnetic bonds J' across the chain, we have studied in detail analytically and iteratively some of the thermodynamic quantities. Particularly interesting is, in the zero-field and zero-temperature limit, the behavior of the magnetization and the susceptibility closely related to the ground-state configurations and their degeneracies. This degeneracy, presented at the condition J' ≤ -J between J and J', explains, also, the existence of nonzero entropy at zero temperature. This model applied as a lattice gas model defined on a tangled chain could be also useful for the experimental investigations in studying the saturation curves for the enzyme kinetics or the melting curves for DNA-denaturation.

Droplet states in quantum XXZ spin systems on general graphs

NASA Astrophysics Data System (ADS)

Fischbacher, C.; Stolz, G.

2018-05-01

We study XXZ spin systems on general graphs. In particular, we describe the formation of droplet states near the bottom of the spectrum in the Ising phase of the model, where the Z-term dominates the XX-term. As key tools, we use particle number conservation of XXZ systems and symmetric products of graphs with their associated adjacency matrices and Laplacians. Of particular interest to us are strips and multi-dimensional Euclidean lattices, for which we discuss the existence of spectral gaps above the droplet regime. We also prove a Combes-Thomas bound which shows that the eigenstates in the droplet regime are exponentially small perturbations of strict (classical) droplets.

Two coupled, driven Ising spin systems working as an engine.

PubMed

Basu, Debarshi; Nandi, Joydip; Jayannavar, A M; Marathe, Rahul

2017-05-01

Miniaturized heat engines constitute a fascinating field of current research. Many theoretical and experimental studies are being conducted that involve colloidal particles in harmonic traps as well as bacterial baths acting like thermal baths. These systems are micron-sized and are subjected to large thermal fluctuations. Hence, for these systems average thermodynamic quantities, such as work done, heat exchanged, and efficiency, lose meaning unless otherwise supported by their full probability distributions. Earlier studies on microengines are concerned with applying Carnot or Stirling engine protocols to miniaturized systems, where system undergoes typical two isothermal and two adiabatic changes. Unlike these models we study a prototype system of two classical Ising spins driven by time-dependent, phase-different, external magnetic fields. These spins are simultaneously in contact with two heat reservoirs at different temperatures for the full duration of the driving protocol. Performance of the model as an engine or a refrigerator depends only on a single parameter, namely the phase between two external drivings. We study this system in terms of fluctuations in efficiency and coefficient of performance (COP). We find full distributions of these quantities numerically and study the tails of these distributions. We also study reliability of the engine. We find the fluctuations dominate mean values of efficiency and COP, and their probability distributions are broad with power law tails.

Two coupled, driven Ising spin systems working as an engine

NASA Astrophysics Data System (ADS)

Basu, Debarshi; Nandi, Joydip; Jayannavar, A. M.; Marathe, Rahul

2017-05-01

Miniaturized heat engines constitute a fascinating field of current research. Many theoretical and experimental studies are being conducted that involve colloidal particles in harmonic traps as well as bacterial baths acting like thermal baths. These systems are micron-sized and are subjected to large thermal fluctuations. Hence, for these systems average thermodynamic quantities, such as work done, heat exchanged, and efficiency, lose meaning unless otherwise supported by their full probability distributions. Earlier studies on microengines are concerned with applying Carnot or Stirling engine protocols to miniaturized systems, where system undergoes typical two isothermal and two adiabatic changes. Unlike these models we study a prototype system of two classical Ising spins driven by time-dependent, phase-different, external magnetic fields. These spins are simultaneously in contact with two heat reservoirs at different temperatures for the full duration of the driving protocol. Performance of the model as an engine or a refrigerator depends only on a single parameter, namely the phase between two external drivings. We study this system in terms of fluctuations in efficiency and coefficient of performance (COP). We find full distributions of these quantities numerically and study the tails of these distributions. We also study reliability of the engine. We find the fluctuations dominate mean values of efficiency and COP, and their probability distributions are broad with power law tails.

Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model

NASA Astrophysics Data System (ADS)

Lang, Johannes; Frank, Bernhard; Halimeh, Jad C.

2018-05-01

We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of nonanalyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of Z2 symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.

Preparing Greenberger-Horne-Zeilinger and W states on a long-range Ising spin model by global controls

NASA Astrophysics Data System (ADS)

Chen, Jiahui; Zhou, Hui; Duan, Changkui; Peng, Xinhua

2017-03-01

Entanglement, a unique quantum resource with no classical counterpart, remains at the heart of quantum information. The Greenberger-Horne-Zeilinger (GHZ) and W states are two inequivalent classes of multipartite entangled states which cannot be transformed into each other by means of local operations and classic communication. In this paper, we present the methods to prepare the GHZ and W states via global controls on a long-range Ising spin model. For the GHZ state, general solutions are analytically obtained for an arbitrary-size spin system, while for the W state, we find a standard way to prepare the W state that is analytically illustrated in three- and four-spin systems and numerically demonstrated for larger-size systems. The number of parameters required in the numerical search increases only linearly with the size of the system.

Mean-field theory on mixed ferro-ferrimagnetic compounds with (A aB bC c) yD

NASA Astrophysics Data System (ADS)

Wei, Guo-Zhu; Xin, Zihua; Liang, Yaqiu; Zhang, Qi

2004-01-01

The magnetic properties of the mixed ferro-ferrimagnetic compounds with (A aB bC c) yD, in which A, B, C and D are four different magnetic ions and form four different sublattices, are studied by using the Ising model. And the Ising model was dealt with standard mean-field approximation. The regions of concentration in which two compensation points or one compensation point exit are given in c- a, b- c and a- b planes. The phase diagrams of the transition temperature Tc and compensation temperature Tcomp are obtained. The temperature dependences of the magnetization are also investigated. Some of the result can be used to explain the experimental work of the molecule-based ferro-ferrimagnet (Ni IIaMn IIbFe IIc) 1.5[Cr III(CN) 6]· zH 2O.

Effective-field renormalization-group method for Ising systems

NASA Astrophysics Data System (ADS)

Fittipaldi, I. P.; De Albuquerque, D. F.

1992-02-01

A new applicable effective-field renormalization-group (ERFG) scheme for computing critical properties of Ising spins systems is proposed and used to study the phase diagrams of a quenched bond-mixed spin Ising model on square and Kagomé lattices. The present EFRG approach yields results which improves substantially on those obtained from standard mean-field renormalization-group (MFRG) method. In particular, it is shown that the EFRG scheme correctly distinguishes the geometry of the lattice structure even when working with the smallest possible clusters, namely N'=1 and N=2.

Controllability of symmetric spin networks

NASA Astrophysics Data System (ADS)

Albertini, Francesca; D'Alessandro, Domenico

2018-05-01

We consider a network of n spin 1/2 systems which are pairwise interacting via Ising interaction and are controlled by the same electro-magnetic control field. Such a system presents symmetries since the Hamiltonian is unchanged if we permute two spins. This prevents full (operator) controllability, in that not every unitary evolution can be obtained. We prove however that controllability is verified if we restrict ourselves to unitary evolutions which preserve the above permutation invariance. For low dimensional cases, n = 2 and n = 3, we provide an analysis of the Lie group of available evolutions and give explicit control laws to transfer between two arbitrary permutation invariant states. This class of states includes highly entangled states such as Greenberger-Horne-Zeilinger (GHZ) states and W states, which are of interest in quantum information.

Immortalization-susceptible elements and their binding factors mediate rejuvenation of regulation of the type I collagenase gene in simian virus 40 large T antigen-transformed immortal human fibroblasts.

PubMed Central

Imai, S; Fujino, T; Nishibayashi, S; Manabe, T; Takano, T

1994-01-01

Dramatic changes occur in expression of the type I collagenase gene during the process of immortalization in simian virus 40 large T antigen-transformed human fibroblasts (S. Imai and T. Takano, Biochem. Biophys. Res. Commun. 189:148-153, 1992). From transient transfection assays, it was determined that these changes involved the functions of two immortalization-susceptible cis-acting elements, ISE1 and ISE2, located in a 100-bp region about 1.7 kb upstream. The profiles of binding of an activator, Proserpine, to the enhancer ISE1 were similar in the extracts of young, senescent preimmortalized and immortalized cells. ISE2 contained both negative and positive regulatory elements located adjacent to each other. The positive regulatory element consisted of a tandem array of putative Ets family- and AP-1-binding sites. An activator, Pluto, interacted with this positive regulatory element and had an AP-1-related component as a complex. The binding activity of Pluto was predominantly detected only in the extract from senescent preimmortalized cells. In contrast, a repressor, Orpheus, which bound to the ATG-rich negative regulatory element of ISE2, was prominently detected in extracts from both young preimmortalized and immortalized cells and appeared to suppress transcription in an orientation-dependent manner. Thus, the interplay of Pluto and Orpheus was suggested to be crucial for regulation of the collagenase gene accompanying in vitro aging and immortalization. Proserpine seemed to interact with Pluto to mediate strong expression of the collagenase gene in cellular senescence. On the basis of these results, we propose a model for regulation of the collagenase gene during in vitro aging and immortalization. Images PMID:7935433

Critical behavior of the anisotropic Heisenberg model by effective-field renormalization group

NASA Astrophysics Data System (ADS)

de Sousa, J. Ricardo; Fittipaldi, I. P.

1994-05-01

A real-space effective-field renormalization-group method (ERFG) recently derived for computing critical properties of Ising spins is extended to treat the quantum spin-1/2 anisotropic Heisenberg model. The formalism is based on a generalized but approximate Callen-Suzuki spin relation and utilizes a convenient differential operator expansion technique. The method is illustrated in several lattice structures by employing its simplest approximation version in which clusters with one (N'=1) and two (N=2) spins are used. The results are compared with those obtained from the standard mean-field (MFRG) and Migdal-Kadanoff (MKRG) renormalization-group treatments and it is shown that this technique leads to rather accurate results. It is shown that, in contrast with the MFRG and MKRG predictions, the EFRG, besides correctly distinguishing the geometries of different lattice structures, also provides a vanishing critical temperature for all two-dimensional lattices in the isotropic Heisenberg limit. For the simple cubic lattice, the dependence of the transition temperature Tc with the exchange anisotropy parameter Δ [i.e., Tc(Δ)], and the resulting value for the critical thermal crossover exponent φ [i.e., Tc≂Tc(0)+AΔ1/φ ] are in quite good agreement with results available in the literature in which more sophisticated treatments are used.

The theory of maximally and minimally even sets, the one- dimensional antiferromagnetic Ising model, and the continued fraction compromise of musical scales

NASA Astrophysics Data System (ADS)

Douthett, Elwood (Jack) Moser, Jr.

1999-10-01

Cyclic configurations of white and black sites, together with convex (concave) functions used to weight path length, are investigated. The weights of the white set and black set are the sums of the weights of the paths connecting the white sites and black sites, respectively, and the weight between sets is the sum of the weights of the paths that connect sites opposite in color. It is shown that when the weights of all configurations of a fixed number of white and a fixed number of black sites are compared, minimum (maximum) weight of a white set, minimum (maximum) weight of the a black set, and maximum (minimum) weight between sets occur simultaneously. Such configurations are called maximally even configurations. Similarly, the configurations whose weights are the opposite extremes occur simultaneously and are called minimally even configurations. Algorithms that generate these configurations are constructed and applied to the one- dimensional antiferromagnetic spin-1/2 Ising model. Next the goodness of continued fractions as applied to musical intervals (frequency ratios and their base 2 logarithms) is explored. It is shown that, for the intermediate convergents between two consecutive principal convergents of an irrational number, the first half of the intermediate convergents are poorer approximations than the preceding principal convergent while the second half are better approximations; the goodness of a middle intermediate convergent can only be determined by calculation. These convergents are used to determine what equal-tempered systems have intervals that most closely approximate the musical fifth (pn/ qn = log2(3/2)). The goodness of exponentiated convergents ( 2pn/qn~3/2 ) is also investigated. It is shown that, with the exception of a middle convergent, the goodness of the exponential form agrees with that of its logarithmic Counterpart As in the case of the logarithmic form, the goodness of a middle intermediate convergent in the exponential form can only be determined by calculation. A Desirability Function is constructed that simultaneously measures how well multiple intervals fit in a given equal-tempered system. These measurements are made for octave (base 2) and tritave systems (base 3). Combinatorial properties important to music modulation are considered. These considerations lead These considerations lead to the construction of maximally even scales as partitions of an equal-tempered system.

Four competing interactions for models with an uncountable set of spin values on a Cayley tree

NASA Astrophysics Data System (ADS)

Rozikov, U. A.; Haydarov, F. H.

2017-06-01

We consider models with four competing interactions ( external field, nearest neighbor, second neighbor, and three neighbors) and an uncountable set [0, 1] of spin values on the Cayley tree of order two. We reduce the problem of describing the splitting Gibbs measures of the model to the problem of analyzing solutions of a nonlinear integral equation and study some particular cases for Ising and Potts models. We also show that periodic Gibbs measures for the given models either are translation invariant or have the period two. We present examples where periodic Gibbs measures with the period two are not unique.

Dynamic magnetic hysteresis properties of two-dimensional ferrimagnetic structures containing high-spin (S = 5/2) and low-spin (S = 1/2)

NASA Astrophysics Data System (ADS)

Batı, Mehmet; Ertaş, Mehmet

2017-09-01

The dynamic hysteresis behaviors of a containing high spin-5/2 and low spin-1/2 Ising ferrimagnetic system on a square lattice are studied by using the dynamic mean-field approximation. The influences of the temperature, the single-ion anisotropy and the frequency on dynamic hysteresis behaviors are investigated in detail. Somewhat characteristic behaviors are found, such as the presence of triple hysteresis loop for appropriate values of the crystal field or temperature. Besides, we observed that, hysteresis loop area and phase transition points are very sensitive to changes in frequency and thus have profound importance in device application.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bogunovic, Hrvoje; Pozo, Jose Maria; Villa-Uriol, Maria Cruz

Purpose: To evaluate the suitability of an improved version of an automatic segmentation method based on geodesic active regions (GAR) for segmenting cerebral vasculature with aneurysms from 3D x-ray reconstruction angiography (3DRA) and time of flight magnetic resonance angiography (TOF-MRA) images available in the clinical routine. Methods: Three aspects of the GAR method have been improved: execution time, robustness to variability in imaging protocols, and robustness to variability in image spatial resolutions. The improved GAR was retrospectively evaluated on images from patients containing intracranial aneurysms in the area of the Circle of Willis and imaged with two modalities: 3DRA andmore » TOF-MRA. Images were obtained from two clinical centers, each using different imaging equipment. Evaluation included qualitative and quantitative analyses of the segmentation results on 20 images from 10 patients. The gold standard was built from 660 cross-sections (33 per image) of vessels and aneurysms, manually measured by interventional neuroradiologists. GAR has also been compared to an interactive segmentation method: isointensity surface extraction (ISE). In addition, since patients had been imaged with the two modalities, we performed an intermodality agreement analysis with respect to both the manual measurements and each of the two segmentation methods. Results: Both GAR and ISE differed from the gold standard within acceptable limits compared to the imaging resolution. GAR (ISE) had an average accuracy of 0.20 (0.24) mm for 3DRA and 0.27 (0.30) mm for TOF-MRA, and had a repeatability of 0.05 (0.20) mm. Compared to ISE, GAR had a lower qualitative error in the vessel region and a lower quantitative error in the aneurysm region. The repeatability of GAR was superior to manual measurements and ISE. The intermodality agreement was similar between GAR and the manual measurements. Conclusions: The improved GAR method outperformed ISE qualitatively as well as quantitatively and is suitable for segmenting 3DRA and TOF-MRA images from clinical routine.« less

In Situ Monitoring of Pb2+ Leaching from the Galvanic Joint Surface in a Prepared Chlorinated Drinking Water.

PubMed

Ma, Xiangmeng; Armas, Stephanie M; Soliman, Mikhael; Lytle, Darren A; Chumbimuni-Torres, Karin; Tetard, Laurene; Lee, Woo Hyoung

2018-02-20

A novel method using a micro-ion-selective electrode (micro-ISE) technique was developed for in situ lead monitoring at the water-metal interface of a brass-leaded solder galvanic joint in a prepared chlorinated drinking water environment. The developed lead micro-ISE (100 μm tip diameter) showed excellent performance toward soluble lead (Pb 2+ ) with sensitivity of 22.2 ± 0.5 mV decade -1 and limit of detection (LOD) of 1.22 × 10 -6 M (0.25 mg L -1 ). The response time was less than 10 s with a working pH range of 2.0-7.0. Using the lead micro-ISE, lead concentration microprofiles were measured from the bulk to the metal surface (within 50 μm) over time. Combined with two-dimensional (2D) pH mapping, this work clearly demonstrated that Pb 2+ ions build-up across the lead anode surface was substantial, nonuniform, and dependent on local surface pH. A large pH gradient (ΔpH = 6.0) developed across the brass and leaded-tin solder joint coupon. Local pH decreases were observed above the leaded solder to a pH as low as 4.0, indicating it was anodic relative to the brass. The low pH above the leaded solder supported elevated lead levels where even small local pH differences of 0.6 units (ΔpH = 0.6) resulted in about four times higher surface lead concentrations (42.9 vs 11.6 mg L -1 ) and 5 times higher fluxes (18.5 × 10 -6 vs 3.5 × 10 -6 mg cm -2 s -1 ). Continuous surface lead leaching monitoring was also conducted for 16 h.

A coherent Ising machine for 2000-node optimization problems

NASA Astrophysics Data System (ADS)

Inagaki, Takahiro; Haribara, Yoshitaka; Igarashi, Koji; Sonobe, Tomohiro; Tamate, Shuhei; Honjo, Toshimori; Marandi, Alireza; McMahon, Peter L.; Umeki, Takeshi; Enbutsu, Koji; Tadanaga, Osamu; Takenouchi, Hirokazu; Aihara, Kazuyuki; Kawarabayashi, Ken-ichi; Inoue, Kyo; Utsunomiya, Shoko; Takesue, Hiroki

2016-11-01

The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.

Finitized conformal spectrum of the Ising model on the cylinder and torus

NASA Astrophysics Data System (ADS)

O'Brien, David L.; Pearce, Paul A.; Ole Warnaar, S.

1996-02-01

The spectrum of the critical Ising model on a lattice with cylindrical and toroidal boundary conditions is calculated by commuting transfer matrix methods. Using a simple truncation procedure, we obtain the natural finitizations of the conformal spectra recently proposed by Melzer. These finitizations imply polynomial identities which in the large lattice limit give rise to the Rogers-Ramanujan identities for the c = {1}/{2} Virasoro characters.

Plasticizer Effects in the PVC Membrane of the Dibasic Phosphate Selective Electrode

PubMed Central

Carey, Clifton

2016-01-01

The PVC membrane of an ion-selective electrode (ISE) sensitive to dibasic phosphate ions (HPO4-ISE) has not been optimized for maximum selectivity, sensitivity, and useable ISE lifetime and further work was necessary to improve its performance. Two areas of investigation are reported here: include the parameters for the lipophilicity of the plasticizer compound used and the amount of cyclic polyamine ionophore incorporated in the PVC membrane. Six candidate plasticizers with a range of lipophilicity were evaluated for their effect on the useable lifetime, sensitivity, and selectivity of the ISE against 13 different anions. Selectivity was determined by a modified fixed interferent method, sensitivity was determined without interferents, and the usable lifetime evaluated at the elapsed time where 50% of the HPO4-ISE failed (L50). The results show that choosing a plasticizer that has a lipophilicity similar to the ionophore's results in the best selectivity and sensitivity and the longest L50. PMID:27347487

Griffiths' inequalities for Ashkin-Teller model

NASA Technical Reports Server (NTRS)

Lee, C. T.

1973-01-01

The two Griffiths' (1967) inequalities for the correlation functions of Ising ferromagnets with two-body interactions, and two other inequalities obtained by Kelly and Sherman (1968) and by Sherman (1969) are shown to hold not only for the Ashkin-Teller (1943) model but also for a generalized Ashkin-Teller model (Kihara et al., 1954) with many-body interactions involving arbitrary clusters of particles. A cluster of particles is understood to mean a collection of pairs of particles rather than a group of particles. The four generalized inequalities under consideration are presented in the form of theorems, and a new inequality is obtained.

Ising versus S U (2) 2 string-net ladder

NASA Astrophysics Data System (ADS)

Vidal, Julien

2018-03-01

We consider the string-net model obtained from S U (2) 2 fusion rules. These fusion rules are shared by two different sets of anyon theories. In this paper, we study the competition between the two corresponding non-Abelian quantum phases in the ladder geometry. A detailed symmetry analysis shows that the nontrivial low-energy sector corresponds to the transverse-field cluster model that displays a critical point described by the s o (2) 1 conformal field theory. Other sectors are obtained by freezing spins in this model.

Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Badiev, M. K., E-mail: m-zagir@mail.ru; Murtazaev, A. K.; Ramazanov, M. K.

2016-10-15

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scalingmore » theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.« less

Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of the s=3/2 Ising model from renormalization-group theory.

PubMed

Yunus, Çağın; Renklioğlu, Başak; Keskin, Mustafa; Berker, A Nihat

2016-06-01

The spin-3/2 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d=3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d=3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model.

Processing Conditions, Thermal and Mechanical Responses of Stretchable Poly (Lactic Acid)/Poly (Butylene Succinate) Films

PubMed Central

Fortunati, Elena; Iannoni, Antonio; Terenzi, Andrea; Torre, Luigi

2017-01-01

Poly (lactic acid) (PLA) and poly (butylene succinate) (PBS) based films containing two different plasticizers [Acetyl Tributyl Citrate (ATBC) and isosorbide diester (ISE)] at three different contents (15 wt %, 20 wt % and 30 wt %) were produced by extrusion method. Thermal, morphological, mechanical and wettability behavior of produced materials was investigated as a function of plasticizer content. Filmature parameters were also adjusted and optimized for different formulations, in order to obtain similar thickness for different systems. Differential scanning calorimeter (DSC) results and evaluation of solubility parameter confirmed that similar miscibility was obtained for ATBC and ISE in PLA, while the two selected plasticizers resulted as not efficient for plasticization of PBS, to the limit that the PBS–30ATBC resulted as not processable. On the basis of these results, isosorbide-based plasticizer was considered a suitable agent for modification of a selected blend (PLA/PBS 80:20) and two mixing approaches were used to identify the role of ISE in the plasticization process: results from mechanical analysis confirmed that both produced PLA–PBS blends (PLA85–ISE15)–PBS20 and (PLA80–PBS20)–ISE15 could guarantee advantages in terms of deformability, with respect to the PLA80–PBS20 reference film, suggesting that the promising use of these stretchable PLA–PBS based films plasticized with isosorbide can provide novel solutions for food packaging applications. PMID:28773168

Monte Carlo Studies of Phase Separation in Compressible 2-dim Ising Models

NASA Astrophysics Data System (ADS)

Mitchell, S. J.; Landau, D. P.

2006-03-01

Using high resolution Monte Carlo simulations, we study time-dependent domain growth in compressible 2-dim ferromagnetic (s=1/2) Ising models with continuous spin positions and spin-exchange moves [1]. Spins interact with slightly modified Lennard-Jones potentials, and we consider a model with no lattice mismatch and one with 4% mismatch. For comparison, we repeat calculations for the rigid Ising model [2]. For all models, large systems (512^2) and long times (10^ 6 MCS) are examined over multiple runs, and the growth exponent is measured in the asymptotic scaling regime. For the rigid model and the compressible model with no lattice mismatch, the growth exponent is consistent with the theoretically expected value of 1/3 [1] for Model B type growth. However, we find that non-zero lattice mismatch has a significant and unexpected effect on the growth behavior.Supported by the NSF.[1] D.P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, second ed. (Cambridge University Press, New York, 2005).[2] J. Amar, F. Sullivan, and R.D. Mountain, Phys. Rev. B 37, 196 (1988).

ISING MODEL OF CHORIOCAPILLARIS FLOW.

PubMed

Spaide, Richard F

2018-01-01

To develop a mathematical model of local blood flow in the choriocapillaris using an Ising model. A JavaScript Ising model was used to create images that emulated the development of signal voids as would be seen in optical coherence tomography angiography of the choriocapillaris. The model was produced by holding the temperature near criticality and varying the field strength. Individual frames were evaluated, and a movie video was created to show the hypothetical development of flow-related signal voids over a lifetime. Much the same as actual choriocapillaris images in humans, the model of flow-related signal voids followed a power-law distribution. The slope and intercept both decreased with age, as is seen in human subjects. This model is a working hypothesis, and as such can help predict system characteristics, evaluate conclusions drawn from studies, suggest new research questions, and provide a way of obtaining an estimate of behavior in which experimental data are not yet available. It may be possible to understand choriocapillaris blood flow in health and disease states by determining by observing deviations from an expected model.

The relation between ferroelasticity and superconductivity

NASA Technical Reports Server (NTRS)

Molak, A.; Manka, R.

1991-01-01

The high-temperature superconductivity is explained widely by the layered crystal structure. The one- and two-dimensional subsystems and their interaction are investigated here. It is assumed that the high-T(sub c) superconductivity takes place in the two-dimensional subsystem and the increase of the phase transition temperature from 60 K up to 90 K is the consequence of turning on the influence of one-dimensional chains. The interaction between the two subsystems is transferred along the c axis by the phonons of breathing mode, which causes the hybridization of the electronic bonds between these subsystems. The experimental works indicate that the existence of both the chains Cu(1)-O and their interaction with the superconducting plane of Cu(2)-O modify the temperature of the transition to the superconducting state. It is seen from the neutron scattering data that the rates of the interatomic distance dependencies on temperature are changed around 240 K and 90 K. The 'zig-zag' order in Cu(1)-O chains has been postulated but, on the other hand, the vibrations with a large amplitude only were reported. The bi-stabilized situation of the oxygen ions can be caused by the change of distance between these ions and the Ba ions. It leads to the appearance of a two-well potential. Its parameters depend on temperature and the dynamics of the oxygen ions' movement. They can induce the antipolar order, which can be, however, more or less chaotic. The investigation of the ferroelastic properties of Y-Ba-Cu-O samples lead to the conclusion that they are related to jumps of ions inside the given chain and not to a diffusion between different sites in the ab plane. Researchers deduce, thus, that the fluctuating oxygen ions from these chains create dipoles in the ab plane. They can be described with the pseudo-spin formalism (- Pauli matrices). The system can be described with the Ising model. The pseudo-spins interact with phonons and influence the superconductivity in the second subsystem.

The relation between ferroelasticity and superconductivity

NASA Technical Reports Server (NTRS)

Molak, A.; Manka, R.

1990-01-01

The high-temperature superconductivity is explained widely by the layered crystal structure. The one- and two-dimensional subsystems and their interaction are investigated here. It is assumed that the high-T(sub c) superconductivity takes place in the two-dimensional subsystem and the increase of the phase transition temperature from 60 K up to 90 K is the consequence of turning on the influence of one-dimensional chains. The interaction between the two subsystems is transferred along the c axis by the phonons of breathing mode, which causes the hybridization of the electronic bonds between these subsystems. The experimental works indicate that the existence of both the chains Cu(1)-O and their interaction with the superconducting plane of Cu(2)-O modify the temperature of the transition to the superconducting state. It is seen from the neutron scattering data that the rates of the interatomic distance dependencies on temperature are changed around 140 K and 90 K. The 'zig-zag' order in Cu(1)-O chains has been postulated but, on the other hand, the vibrations with a large amplitude only were reported. The bi-stabilized situation of the oxygen ions can be caused by the change of distance between these ions and the Ba ions. It leads to the appearance of a two-well potential. Its parameters depend on temperature and the dynamics of the oxygen ions' movement. They can induce the antipolar order, which can be, however, more or less chaotic. The investigation of the ferroelastic properties of Y-Ba-Cu-O samples lead to the conclusion that they are related to jumps of ions inside the given chain and not to a diffusion between different sites in the ab plane. Researchers deduce thus that the fluctuating oxygen ions from these chains create dipoles in the ab plane. They can be described with the pseudo-spin formalism/ - Pauli matrices/. The system can be described with the Ising model. The pseudo-spins interact with phonons and influence the superconductivity in the second subsystem.

Z n clock models and chains of so(n)2 non-Abelian anyons: symmetries, integrable points and low energy properties

NASA Astrophysics Data System (ADS)

Finch, Peter E.; Flohr, Michael; Frahm, Holger

2018-02-01

We study two families of quantum models which have been used previously to investigate the effect of topological symmetries in one-dimensional correlated matter. Various striking similarities are observed between certain {Z}n quantum clock models, spin chains generalizing the Ising model, and chains of non-Abelian anyons constructed from the so(n)2 fusion category for odd n, both subject to periodic boundary conditions. In spite of the differences between these two types of quantum chains, e.g. their Hilbert spaces being spanned by tensor products of local spin states or fusion paths of anyons, the symmetries of the lattice models are shown to be closely related. Furthermore, under a suitable mapping between the parameters describing the interaction between spins and anyons the respective Hamiltonians share part of their energy spectrum (although their degeneracies may differ). This spin-anyon correspondence can be extended by fine-tuning of the coupling constants leading to exactly solvable models. We show that the algebraic structures underlying the integrability of the clock models and the anyon chain are the same. For n  =  3,5,7 we perform an extensive finite size study—both numerical and based on the exact solution—of these models to map out their ground state phase diagram and to identify the effective field theories describing their low energy behaviour. We observe that the continuum limit at the integrable points can be described by rational conformal field theories with extended symmetry algebras which can be related to the discrete ones of the lattice models.

Yang-Baxter and other relations for free-fermion and Ising models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davies, B.

1987-02-01

Eight-vertex, free fermion, and Ising models are formulated using a convention that emphasizes the algebra of the local transition operators that arise in the quantum inverse method. Equivalent classes of models, are investigated, with particular emphasis on the role of the star-triangle relations. Using these results, a natural and symmetrical parametrization is introduced and Yang-Baxter relations are constructed in an elementary way. The paper concludes with a consideration of duality, which links the present work to a recent paper of Baxter on the free fermion model.

Magnetic structure and dispersion relation of the S = 1 2 quasi-one-dimensional Ising-like antiferromagnet BaCo 2 V 2 O 8 in a transverse magnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matsuda, M.; Onishi, H.; Okutani, A.

Here, BaCo 2V 2O 8 consists of Co chains in which a Co 2+ ion carries a fictitious spin 1/2 with Ising anisotropy. We performed elastic and inelastic neutron scattering experiments in BaCo 2V 2O 8 in a magnetic field perpendicular to the c axis which is the chain direction. With applying magnetic field along the a axis at 3.5 K, the antiferromagnetic order with the easy axis along the c axis, observed in zero magnetic field, is completely suppressed at 8 T, while the magnetic field gradually induces an antiferromagnetic order with the spin component along the b axis.more » We also studied magnetic excitations as a function of transverse magnetic field. The lower boundary of the spinon excitations splits gradually with increasing magnetic field. The overall feature of the magnetic excitation spectra in the magnetic field is reproduced by the theoretical calculation based on the spin 1/2 XXZ antiferromagnetic chain model, which predicts that the dynamic magnetic structure factor of the spin component along the chain direction is enhanced and that along the field direction has clear incommensurate correlations.« less

Magnetic structure and dispersion relation of the S = 1 2 quasi-one-dimensional Ising-like antiferromagnet BaCo 2 V 2 O 8 in a transverse magnetic field

DOE PAGES

Matsuda, M.; Onishi, H.; Okutani, A.; ...

2017-07-25

Here, BaCo 2V 2O 8 consists of Co chains in which a Co 2+ ion carries a fictitious spin 1/2 with Ising anisotropy. We performed elastic and inelastic neutron scattering experiments in BaCo 2V 2O 8 in a magnetic field perpendicular to the c axis which is the chain direction. With applying magnetic field along the a axis at 3.5 K, the antiferromagnetic order with the easy axis along the c axis, observed in zero magnetic field, is completely suppressed at 8 T, while the magnetic field gradually induces an antiferromagnetic order with the spin component along the b axis.more » We also studied magnetic excitations as a function of transverse magnetic field. The lower boundary of the spinon excitations splits gradually with increasing magnetic field. The overall feature of the magnetic excitation spectra in the magnetic field is reproduced by the theoretical calculation based on the spin 1/2 XXZ antiferromagnetic chain model, which predicts that the dynamic magnetic structure factor of the spin component along the chain direction is enhanced and that along the field direction has clear incommensurate correlations.« less

Magnetic structure and dispersion relation of the S =1/2 quasi-one-dimensional Ising-like antiferromagnet BaCo2V2O8 in a transverse magnetic field

NASA Astrophysics Data System (ADS)

Matsuda, M.; Onishi, H.; Okutani, A.; Ma, J.; Agrawal, H.; Hong, T.; Pajerowski, D. M.; Copley, J. R. D.; Okunishi, K.; Mori, M.; Kimura, S.; Hagiwara, M.

2017-07-01

BaCo2V2O8 consists of Co chains in which a Co2 + ion carries a fictitious spin 1/2 with Ising anisotropy. We performed elastic and inelastic neutron scattering experiments in BaCo2V2O8 in a magnetic field perpendicular to the c axis which is the chain direction. With applying magnetic field along the a axis at 3.5 K, the antiferromagnetic order with the easy axis along the c axis, observed in zero magnetic field, is completely suppressed at 8 T, while the magnetic field gradually induces an antiferromagnetic order with the spin component along the b axis. We also studied magnetic excitations as a function of transverse magnetic field. The lower boundary of the spinon excitations splits gradually with increasing magnetic field. The overall feature of the magnetic excitation spectra in the magnetic field is reproduced by the theoretical calculation based on the spin 1/2 X X Z antiferromagnetic chain model, which predicts that the dynamic magnetic structure factor of the spin component along the chain direction is enhanced and that along the field direction has clear incommensurate correlations.

Quantum-information approach to the Ising model: Entanglement in chains of qubits

NASA Astrophysics Data System (ADS)

Štelmachovič, Peter; Bužek, Vladimír

2004-09-01

Simple physical interactions between spin- 1/2 particles may result in quantum states that exhibit exotic correlations that are difficult to find if one simply explores state spaces of multipartite systems. In particular, we present a detailed investigation of the well-known Ising model of a chain (ring) of spin- 1/2 particles (qubits) in a transverse magnetic field. We present explicit expressions for eigenstates of the model Hamiltonian for arbitrary number of spin- 1/2 particles in the chain in the standard (computer) basis, and we investigate quantum entanglement between individual qubits. We analyze bipartite as well as multipartite entanglement in the ground state of the model. In particular, we show that bipartite entanglement between pairs of qubits of the Ising chain (measured in terms of a concurrence) as a function of the parameter λ has a maximum around the point λ=1 , and it monotonically decreases for large values of λ . We prove that in the limit λ→∞ this state is locally unitary equivalent to an N -partite Greenberger-Horn-Zeilinger state. We also analyze a very specific eigenstate of the Ising Hamiltonian with a zero eigenenergy (we denote this eigenstate as the X -state). This X -state exhibits the “extreme” entanglement in a sense that an arbitrary subset A of k⩽n qubits in the Ising chain composed of N=2n+1 qubits is maximally entangled with the remaining qubits (set B ) in the chain. In addition, we prove that by performing a local operation just on the subset B , one can transform the X -state into a direct product of k singlets shared by the parties A and B . This property of the X -state can be utilized for new secure multipartite communication protocols.

Interaction modifiers in artificial spin ices

DOE PAGES

Ostman, Erik; Stopfel, Henry; Chioar, Ioan -Augustin; ...

2018-02-12

The modification of geometry and interactions in two-dimensional magnetic nanosystems has enabled a range of studies addressing the magnetic order, collective low-energy dynamics and emergent magnetic properties in, for example, artificial spin-ice structures. The common denominator of all these investigations is the use of Ising-like mesospins as building blocks, in the form of elongated magnetic islands. Here, we introduce a new approach: single interaction modifiers, using slave mesospins in the form of discs, within which the mesospin is free to rotate in the disc plane1. We show that by placing these on the vertices of square artificial spin-ice arrays andmore » varying their diameter, it is possible to tailor the strength and the ratio of the interaction energies. We demonstrate the existence of degenerate ice-rule-obeying states in square artificial spin-ice structures, enabling the exploration of thermal dynamics in a spin-liquid manifold. Furthermore, we even observe the emergence of flux lattices on larger length scales, when the energy landscape of the vertices is reversed. In conclusion, the work highlights the potential of a design strategy for two-dimensional magnetic nano-architectures, through which mixed dimensionality of mesospins can be used to promote thermally emergent mesoscale magnetic states.« less

Interaction modifiers in artificial spin ices

NASA Astrophysics Data System (ADS)

Ã-stman, Erik; Stopfel, Henry; Chioar, Ioan-Augustin; Arnalds, Unnar B.; Stein, Aaron; Kapaklis, Vassilios; Hjörvarsson, Björgvin

2018-04-01

The modification of geometry and interactions in two-dimensional magnetic nanosystems has enabled a range of studies addressing the magnetic order1-6, collective low-energy dynamics7,8 and emergent magnetic properties5, 9,10 in, for example, artificial spin-ice structures. The common denominator of all these investigations is the use of Ising-like mesospins as building blocks, in the form of elongated magnetic islands. Here, we introduce a new approach: single interaction modifiers, using slave mesospins in the form of discs, within which the mesospin is free to rotate in the disc plane11. We show that by placing these on the vertices of square artificial spin-ice arrays and varying their diameter, it is possible to tailor the strength and the ratio of the interaction energies. We demonstrate the existence of degenerate ice-rule-obeying states in square artificial spin-ice structures, enabling the exploration of thermal dynamics in a spin-liquid manifold. Furthermore, we even observe the emergence of flux lattices on larger length scales, when the energy landscape of the vertices is reversed. The work highlights the potential of a design strategy for two-dimensional magnetic nano-architectures, through which mixed dimensionality of mesospins can be used to promote thermally emergent mesoscale magnetic states.

Interaction modifiers in artificial spin ices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ostman, Erik; Stopfel, Henry; Chioar, Ioan -Augustin

The modification of geometry and interactions in two-dimensional magnetic nanosystems has enabled a range of studies addressing the magnetic order, collective low-energy dynamics and emergent magnetic properties in, for example, artificial spin-ice structures. The common denominator of all these investigations is the use of Ising-like mesospins as building blocks, in the form of elongated magnetic islands. Here, we introduce a new approach: single interaction modifiers, using slave mesospins in the form of discs, within which the mesospin is free to rotate in the disc plane1. We show that by placing these on the vertices of square artificial spin-ice arrays andmore » varying their diameter, it is possible to tailor the strength and the ratio of the interaction energies. We demonstrate the existence of degenerate ice-rule-obeying states in square artificial spin-ice structures, enabling the exploration of thermal dynamics in a spin-liquid manifold. Furthermore, we even observe the emergence of flux lattices on larger length scales, when the energy landscape of the vertices is reversed. In conclusion, the work highlights the potential of a design strategy for two-dimensional magnetic nano-architectures, through which mixed dimensionality of mesospins can be used to promote thermally emergent mesoscale magnetic states.« less

A Q-Ising model application for linear-time image segmentation

NASA Astrophysics Data System (ADS)

Bentrem, Frank W.

2010-10-01

A computational method is presented which efficiently segments digital grayscale images by directly applying the Q-state Ising (or Potts) model. Since the Potts model was first proposed in 1952, physicists have studied lattice models to gain deep insights into magnetism and other disordered systems. For some time, researchers have realized that digital images may be modeled in much the same way as these physical systems ( i.e., as a square lattice of numerical values). A major drawback in using Potts model methods for image segmentation is that, with conventional methods, it processes in exponential time. Advances have been made via certain approximations to reduce the segmentation process to power-law time. However, in many applications (such as for sonar imagery), real-time processing requires much greater efficiency. This article contains a description of an energy minimization technique that applies four Potts (Q-Ising) models directly to the image and processes in linear time. The result is analogous to partitioning the system into regions of four classes of magnetism. This direct Potts segmentation technique is demonstrated on photographic, medical, and acoustic images.

Machine learning–enabled identification of material phase transitions based on experimental data: Exploring collective dynamics in ferroelectric relaxors

DOE PAGES

Li, Linglong; Yang, Yaodong; Zhang, Dawei; ...

2018-03-30

Exploration of phase transitions and construction of associated phase diagrams are of fundamental importance for condensed matter physics and materials science alike, and remain the focus of extensive research for both theoretical and experimental studies. For the latter, comprehensive studies involving scattering, thermodynamics, and modeling are typically required. We present a new approach to data mining multiple realizations of collective dynamics, measured through piezoelectric relaxation studies, to identify the onset of a structural phase transition in nanometer-scale volumes, that is, the probed volume of an atomic force microscope tip. Machine learning is used to analyze the multidimensional data sets describingmore » relaxation to voltage and thermal stimuli, producing the temperature-bias phase diagram for a relaxor crystal without the need to measure (or know) the order parameter. The suitability of the approach to determine the phase diagram is shown with simulations based on a two-dimensional Ising model. Finally, these results indicate that machine learning approaches can be used to determine phase transitions in ferroelectrics, providing a general, statistically significant, and robust approach toward determining the presence of critical regimes and phase boundaries.« less

Machine learning–enabled identification of material phase transitions based on experimental data: Exploring collective dynamics in ferroelectric relaxors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Linglong; Yang, Yaodong; Zhang, Dawei

Exploration of phase transitions and construction of associated phase diagrams are of fundamental importance for condensed matter physics and materials science alike, and remain the focus of extensive research for both theoretical and experimental studies. For the latter, comprehensive studies involving scattering, thermodynamics, and modeling are typically required. We present a new approach to data mining multiple realizations of collective dynamics, measured through piezoelectric relaxation studies, to identify the onset of a structural phase transition in nanometer-scale volumes, that is, the probed volume of an atomic force microscope tip. Machine learning is used to analyze the multidimensional data sets describingmore » relaxation to voltage and thermal stimuli, producing the temperature-bias phase diagram for a relaxor crystal without the need to measure (or know) the order parameter. The suitability of the approach to determine the phase diagram is shown with simulations based on a two-dimensional Ising model. Finally, these results indicate that machine learning approaches can be used to determine phase transitions in ferroelectrics, providing a general, statistically significant, and robust approach toward determining the presence of critical regimes and phase boundaries.« less

Critical behavior of quasi-two-dimensional semiconducting ferromagnet Cr 2 Ge 2 Te 6

DOE PAGES

Liu, Yu; Petrovic, C.

2017-08-03

Some critical properties of the single-crystalline semiconducting ferromagnet Cr 2 Ge 2 Te 6 were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic phase transition. Critical exponents β = 0.200 ± 0.003 with a critical temperature T c = 62.65 ± 0.07 K and γ = 1.28 ± 0.03 with T c = 62.75 ± 0.06 K are obtained by the Kouvel-Fisher method whereas δ = 7.96 ± 0.01 is obtained by a critical isotherm analysis at T c = 62.7 K. These critical exponents obey the Widom scaling relation δ = 1 + γ / β ,more » indicating self-consistency of the obtained values. Furthermore, with these critical exponents the isotherm M ( H ) curves below and above the critical temperatures collapse into two independent universal branches, obeying the single scaling equation m = f ± ( h ) , where m and h are renormalized magnetization and field, respectively. The determined exponents match well with those calculated from the results of the renormalization group approach for a two-dimensional Ising system coupled with a long-range interaction between spins decaying as J ( r ) ≈ r - ( d + σ ) with σ = 1.52 .« less

Rotational symmetry breaking toward a string-valence bond solid phase in frustrated J1 -J2 transverse field Ising model

NASA Astrophysics Data System (ADS)

Sadrzadeh, M.; Langari, A.

2018-06-01

We study the effect of quantum fluctuations by means of a transverse magnetic field (Γ) on the highly degenerate ground state of antiferromagnetic J1 -J2 Ising model on the square lattice, at the limit J2 /J1 = 0.5 . We show that harmonic quantum fluctuations based on single spin flips can not lift such degeneracy, however an-harmonic quantum fluctuations based on multi spin cluster flip excitations lift the degeneracy toward a unique ground state with string-valence bond solid (VBS) nature. A cluster operator formalism has been implemented to incorporate an-harmonic quantum fluctuations. We show that cluster-type excitations of the model lead not only to lower the excitation energy compared with a single-spin flip but also to lift the extensive degeneracy in favor of a string-VBS state, which breaks lattice rotational symmetry with only two fold degeneracy. The tendency toward the broken symmetry state is justified by numerical exact diagonalization. Moreover, we introduce a map to find the relation between the present model on the checkerboard and square lattices.

A Generalized 2D-Dynamical Mean-Field Ising Model with a Rich Set of Bifurcations (Inspired and Applied to Financial Crises)

NASA Astrophysics Data System (ADS)

Smug, Damian; Sornette, Didier; Ashwin, Peter

We analyze an extended version of the dynamical mean-field Ising model. Instead of classical physical representation of spins and external magnetic field, the model describes traders' opinion dynamics. The external field is endogenized to represent a smoothed moving average of the past state variable. This model captures in a simple set-up the interplay between instantaneous social imitation and past trends in social coordinations. We show the existence of a rich set of bifurcations as a function of the two parameters quantifying the relative importance of instantaneous versus past social opinions on the formation of the next value of the state variable. Moreover, we present a thorough analysis of chaotic behavior, which is exhibited in certain parameter regimes. Finally, we examine several transitions through bifurcation curves and study how they could be understood as specific market scenarios. We find that the amplitude of the corrections needed to recover from a crisis and to push the system back to “normal” is often significantly larger than the strength of the causes that led to the crisis itself.

Topological entanglement entropy with a twist.

PubMed

Brown, Benjamin J; Bartlett, Stephen D; Doherty, Andrew C; Barrett, Sean D

2013-11-27

Defects in topologically ordered models have interesting properties that are reminiscent of the anyonic excitations of the models themselves. For example, dislocations in the toric code model are known as twists and possess properties that are analogous to Ising anyons. We strengthen this analogy by using the topological entanglement entropy as a diagnostic tool to identify properties of both defects and excitations in the toric code. Specifically, we show, through explicit calculation, that the toric code model including twists and dyon excitations has the same quantum dimensions, the same total quantum dimension, and the same fusion rules as an Ising anyon model.

Different as night and day: Patterns of isolated seizures, clusters, and status epilepticus.

PubMed

Goldenholz, Daniel M; Rakesh, Kshitiz; Kapur, Kush; Gaínza-Lein, Marina; Hodgeman, Ryan; Moss, Robert; Theodore, William H; Loddenkemper, Tobias

2018-05-01

Using approximations based on presumed U.S. time zones, we characterized day and nighttime seizure patterns in a patient-reported database, Seizure Tracker. A total of 632 995 seizures (9698 patients) were classified into 4 categories: isolated seizure event (ISE), cluster without status epilepticus (CWOS), cluster including status epilepticus (CIS), and status epilepticus (SE). We used a multinomial mixed-effects logistic regression model to calculate odds ratios (ORs) to determine night/day ratios for the difference between seizure patterns: ISE versus SE, ISE versus CWOS, ISE versus CIS, and CWOS versus CIS. Ranges of OR values were reported across cluster definitions. In adults, ISE was more likely at night compared to CWOS (OR = 1.49, 95% adjusted confidence interval [CI] = 1.36-1.63) and to CIS (OR = 1.61, 95% adjusted CI = 1.34-1.88). The ORs for ISE versus SE and CWOS versus SE were not significantly different regardless of cluster definition. In children, ISE was less likely at night compared to SE (OR = 0.85, 95% adjusted CI = 0.79-0.91). ISE was more likely at night compared to CWOS (OR = 1.35, 95% adjusted CI = 1.26-1.44) and CIS (OR = 1.65, 95% adjusted CI = 1.44-1.86). CWOS was more likely during the night compared to CIS (OR = 1.22, 95% adjusted CI = 1.05-1.39). With the exception of SE in children, our data suggest that more severe patterns favor daytime. This suggests distinct day/night preferences for different seizure patterns in children and adults. Wiley Periodicals, Inc. © 2018 International League Against Epilepsy.

Ibervillea sonorae (Cucurbitaceae) induces the glucose uptake in human adipocytes by activating a PI3K-independent pathway.

PubMed

Zapata-Bustos, Rocio; Alonso-Castro, Angel Josabad; Gómez-Sánchez, Maricela; Salazar-Olivo, Luis A

2014-03-28

Ibervillea sonorae (S. Watson) Greene (Cucurbitaceae), a plant used for the empirical treatment of type 2 diabetes in México, exerts antidiabetic effects on animal models but its mechanism of action remains unknown. The aim of this study is to investigate the antidiabetic mechanism of an Ibervillea sonorae aqueous extract (ISE). Non-toxic ISE concentrations were assayed on the glucose uptake by insulin-sensitive and insulin-resistant murine and human cultured adipocytes, both in the absence or the presence of insulin signaling pathway inhibitors, and on murine and human adipogenesis. Chemical composition of ISE was examined by spectrophotometric and HPLC techniques. ISE stimulated the 2-NBDGlucose uptake by mature adipocytes in a concentration-dependent manner. ISE 50 µg/ml induced the 2-NBDG uptake in insulin-sensitive 3T3-F442A, 3T3-L1 and human adipocytes by 100%, 63% and 33%, compared to insulin control. Inhibitors for the insulin receptor, PI3K, AKT and GLUT4 blocked the 2-NBDG uptake in murine cells, but human adipocytes were insensitive to the PI3K inhibitor Wortmannin. ISE 50 µg/ml also stimulated the 2-NBDG uptake in insulin-resistant adipocytes by 117% (3T3-F442A), 83% (3T3-L1) and 48% (human). ISE induced 3T3-F442A adipogenesis but lacked proadipogenic effects on 3T3-L1 and human preadipocytes. Chemical analyses showed the presence of phenolics in ISE, mainly an appreciable concentration of gallic acid. Ibervillea sonorae exerts its antidiabetic properties by means of hydrosoluble compounds stimulating the glucose uptake in human preadipocytes by a PI3K-independent pathway and without proadipogenic effects. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Transfer-matrix study of a hard-square lattice gas with two kinds of particles and density anomaly

NASA Astrophysics Data System (ADS)

Oliveira, Tiago J.; Stilck, Jürgen F.

2015-09-01

Using transfer matrix and finite-size scaling methods, we study the thermodynamic behavior of a lattice gas with two kinds of particles on the square lattice. Only excluded volume interactions are considered, so that the model is athermal. Large particles exclude the site they occupy and its four first neighbors, while small particles exclude only their site. Two thermodynamic phases are found: a disordered phase where large particles occupy both sublattices with the same probability and an ordered phase where one of the two sublattices is preferentially occupied by them. The transition between these phases is continuous at small concentrations of the small particles and discontinuous at larger concentrations, both transitions are separated by a tricritical point. Estimates of the central charge suggest that the critical line is in the Ising universality class, while the tricritical point has tricritical Ising (Blume-Emery-Griffiths) exponents. The isobaric curves of the total density as functions of the fugacity of small or large particles display a minimum in the disordered phase.

Maximally informative pairwise interactions in networks

PubMed Central

Fitzgerald, Jeffrey D.; Sharpee, Tatyana O.

2010-01-01

Several types of biological networks have recently been shown to be accurately described by a maximum entropy model with pairwise interactions, also known as the Ising model. Here we present an approach for finding the optimal mappings between input signals and network states that allow the network to convey the maximal information about input signals drawn from a given distribution. This mapping also produces a set of linear equations for calculating the optimal Ising-model coupling constants, as well as geometric properties that indicate the applicability of the pairwise Ising model. We show that the optimal pairwise interactions are on average zero for Gaussian and uniformly distributed inputs, whereas they are nonzero for inputs approximating those in natural environments. These nonzero network interactions are predicted to increase in strength as the noise in the response functions of each network node increases. This approach also suggests ways for how interactions with unmeasured parts of the network can be inferred from the parameters of response functions for the measured network nodes. PMID:19905153

Improving Health Care Providers' Capacity for Self-Regulated Learning in Online Continuing Pharmacy Education: The Role of Internet Self-Efficacy.

PubMed

Chiu, Yen-Lin; Liang, Jyh-Chong; Mao, Pili Chih-Min; Tsai, Chin-Chung

2016-01-01

Although Internet-based learning is widely used to improve health professionals' knowledge and skills, the self-regulated learning (SRL) activities of online continuing education in pharmacy are seldom discussed. The main purpose of this study was to explore the relationships between pharmacists' Internet self-efficacy (ISE) and their SRL in online continuing education. A total of 164 in-service pharmacists in Taiwan were surveyed with the Internet Self-Efficacy Survey, including basic ISE (B-ISE), advanced ISE (A-ISE) and professional ISE (P-ISE), as well as the Self-Regulated Learning Questionnaire consisting of preparatory SRL (P-SRL) and enactment SRL (E-SRL). Results of a 1-by-3 (educational levels: junior college versus bachelor versus master) analysis of variance and a 1-by-4 (institutions: community-based versus hospital versus clinic versus company) analysis of variance revealed that there were differences in ISE and SRL among different education levels and working institutions. The hierarchical regression analyses indicated that B-ISE and P-ISE were significant predictors of P-SRL, whereas P-ISE was a critical predictor of E-SRL. Moreover, the interaction of P-ISE × age was linked to E-SRL, implying that P-ISE has a stronger influence on E-SRL for older pharmacists than for younger pharmacists. However, the interactions between age and ISE (A-ISE, B-ISE, and P-ISE) were not related to P-SRL. This study highlighted the importance of ISE and age for increasing pharmacists' SRL in online continuing education.

Implicit and Explicit Self-Esteem in Current, Remitted, Recovered, and Comorbid Depression and Anxiety Disorders: The NESDA Study.

PubMed

van Tuijl, Lonneke A; Glashouwer, Klaske A; Bockting, Claudi L H; Tendeiro, Jorge N; Penninx, Brenda W J H; de Jong, Peter J

2016-01-01

Dual processing models of psychopathology emphasize the relevance of differentiating between deliberative self-evaluative processes (explicit self-esteem; ESE) and automatically-elicited affective self-associations (implicit self-esteem; ISE). It has been proposed that both low ESE and ISE would be involved in major depressive disorder (MDD) and anxiety disorders (AD). Further, it has been hypothesized that MDD and AD may result in a low ISE "scar" that may contribute to recurrence after remission. However, the available evidence provides no straightforward support for the relevance of low ISE in MDD/AD, and studies testing the relevance of discrepant SE even showed that especially high ISE combined with low ESE is predictive of the development of internalizing symptoms. However, these earlier findings have been limited by small sample sizes, poorly defined groups in terms of comorbidity and phase of the disorders, and by using inadequate indices of discrepant SE. Therefore, this study tested further the proposed role of ISE and discrepant SE in a large-scale study allowing for stricter differentiation between groups and phase of disorder. In the context of the Netherlands Study of Depression and Anxiety (NESDA), we selected participants with current MDD (n = 60), AD (n = 111), and comorbid MDD/AD (n = 71), remitted MDD (n = 41), AD (n = 29), and comorbid MDD/AD (n = 14), recovered MDD (n = 136) and AD (n = 98), and never MDD or AD controls (n = 382). The Implicit Association Test was used to index ISE and the Rosenberg Self-Esteem Scale indexed ESE. Controls reported higher ESE than all other groups, and current comorbid MDD/AD had lower ESE than all other clinical groups. ISE was only lower than controls in current comorbid AD/MDD. Discrepant self-esteem (difference between ISE and ESE) was not associated with disorder status once controlling for ESE. Cross-sectional design limits causal inferences. Findings suggest a prominent role for ESE in MDD and AD, while in comorbid MDD/AD negative self-evaluations are also present at the implicit level. There was no evidence to support the view that AD and MDD would result in a low ISE "scar".

Enhanced multi-protocol analysis via intelligent supervised embedding (EMPrAvISE): detecting prostate cancer on multi-parametric MRI

NASA Astrophysics Data System (ADS)

Viswanath, Satish; Bloch, B. Nicholas; Chappelow, Jonathan; Patel, Pratik; Rofsky, Neil; Lenkinski, Robert; Genega, Elizabeth; Madabhushi, Anant

2011-03-01

Currently, there is significant interest in developing methods for quantitative integration of multi-parametric (structural, functional) imaging data with the objective of building automated meta-classifiers to improve disease detection, diagnosis, and prognosis. Such techniques are required to address the differences in dimensionalities and scales of individual protocols, while deriving an integrated multi-parametric data representation which best captures all disease-pertinent information available. In this paper, we present a scheme called Enhanced Multi-Protocol Analysis via Intelligent Supervised Embedding (EMPrAvISE); a powerful, generalizable framework applicable to a variety of domains for multi-parametric data representation and fusion. Our scheme utilizes an ensemble of embeddings (via dimensionality reduction, DR); thereby exploiting the variance amongst multiple uncorrelated embeddings in a manner similar to ensemble classifier schemes (e.g. Bagging, Boosting). We apply this framework to the problem of prostate cancer (CaP) detection on 12 3 Tesla pre-operative in vivo multi-parametric (T2-weighted, Dynamic Contrast Enhanced, and Diffusion-weighted) magnetic resonance imaging (MRI) studies, in turn comprising a total of 39 2D planar MR images. We first align the different imaging protocols via automated image registration, followed by quantification of image attributes from individual protocols. Multiple embeddings are generated from the resultant high-dimensional feature space which are then combined intelligently to yield a single stable solution. Our scheme is employed in conjunction with graph embedding (for DR) and probabilistic boosting trees (PBTs) to detect CaP on multi-parametric MRI. Finally, a probabilistic pairwise Markov Random Field algorithm is used to apply spatial constraints to the result of the PBT classifier, yielding a per-voxel classification of CaP presence. Per-voxel evaluation of detection results against ground truth for CaP extent on MRI (obtained by spatially registering pre-operative MRI with available whole-mount histological specimens) reveals that EMPrAvISE yields a statistically significant improvement (AUC=0.77) over classifiers constructed from individual protocols (AUC=0.62, 0.62, 0.65, for T2w, DCE, DWI respectively) as well as one trained using multi-parametric feature concatenation (AUC=0.67).

Disappearance of Ising nature in Ca3ZnMnO6 studied by high-field ESR.

PubMed

Ruan, M Y; Ouyang, Z W; Guo, Y M; Cheng, J J; Sun, Y C; Xia, Z C; Rao, G H; Okubo, S; Ohta, H

2014-06-11

High-field electron spin resonance measurements of an antiferromagnet Ca3ZnMnO6 isostructure, with the Ising-chain multiferroic Ca3CoMnO6, have been carried out. Two distinct resonance modes were observed below TN = 25 K, which is well explained by conventional antiferromagnetic resonance theory with easy-plane anisotropy. The zero-field spin gap is derived to be about 166 GHz, originating from the easy-plane anisotropy and exchange interaction. Our result suggests that the Dzyaloshinsky-Moriya interaction, which may induce spin canting, is absent. Disappearance of Ising anisotropy in Ca3ZnMnO6 suggests that the Co(4+) ion, as well as the Co-Mn superexchange, plays an important role for the Ising nature in Ca3CoMnO6.

Reconnection at the earth's magnetopause - Magnetic field observations and flux transfer events

NASA Technical Reports Server (NTRS)

Russell, C. T.

1984-01-01

Theoretical models of plasma acceleration by magnetic-field-line reconnection at the earth magnetopause and the high-resolution three-dimensional plasma measurements obtained with the ISEE satellites are compared and illustrated with diagrams, graphs, drawings, and histograms. The history of reconnection theory and the results of early satellite observations are summarized; the thickness of the magnetopause current layer is discussed; problems in analyzing the polarization of current-layer rotation are considered; and the flux-transfer events responsible for periods of patchy reconnection are characterized in detail. The need for further observations and refinements of the theory to explain the initiation of reconnection and identify the mechanism determining whether it is patchy or steady-state is indicated.

Localization Protection and Symmetry Breaking in One-dimensional Potts Chains

NASA Astrophysics Data System (ADS)

Friedman, Aaron; Vasseur, Romain; Potter, Andrew; Parameswaran, Siddharth

Recent work on the 3-state Potts and Z3 clock models has demonstrated that their ordered phases are connected by duality to a phase that hosts topologically protected parafermionic zero modes at the system's boundary. The analogy with Kitaev's example of the one-dimensional Majorana chain (similarly related by duality to the Ising model) suggests that such zero modes may also be stabilized in highly excited states by many-body localization (MBL). However, the Potts model has a non-Abelian S3 symmetry believed to be incompatible with MBL; hence any MBL state must spontaneously break this symmetry, either completely or into one of its abelian subgroups (Z2 or Z3), with the topological phase corresponding to broken Z3 symmetry. We therefore study the excited state phase structure of random three-state Potts and clock models in one dimension using exact diagonalization and real-space renormalization group techniques. We also investigate the interesting possibility of a direct excited-state transition between MBL phases that break either Z3 or Z2 symmetry, forbidden within Landau theory. NSF DGE-1321846 (AJF), NSF DMR-1455366 and President's Research Catalyst Award No. CA-15-327861 from the University of California Office of the President (SAP), LDRD Program of LBNL (RV), NSF PHY11-25915 at the KITP (AJF, RV, SAP).

Inference of the sparse kinetic Ising model using the decimation method

NASA Astrophysics Data System (ADS)

Decelle, Aurélien; Zhang, Pan

2015-05-01

In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in Decelle and Ricci-Tersenghi [Phys. Rev. Lett. 112, 070603 (2014), 10.1103/PhysRevLett.112.070603] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively. During the decimation process the likelihood function is maximized over the remaining couplings. Unlike the ℓ1-optimization-based methods, the decimation method does not use the Laplace distribution as a heuristic choice of prior to select a sparse solution. In our case, the whole process can be done auto-matically without fixing any parameters by hand. We show that in the dynamical inference problem, where the task is to reconstruct the couplings of an Ising model given the data, the decimation process can be applied naturally into a maximum-likelihood optimization algorithm, as opposed to the static case where pseudolikelihood method needs to be adopted. We also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems. Our results illustrate that, on various topologies and with different distribution of couplings, the decimation method outperforms the widely used ℓ1-optimization-based methods.

The Pioneer 11 1976 solar conjunction: A unique opportunity to explore the heliographic latitudinal variations of the solar corona

NASA Technical Reports Server (NTRS)

Berman, A. L.; Wackley, J. A.; Rockwell, S. T.; Yee, J. G.

1976-01-01

The 1976 Pioneer II Solar Conjunction provided the opportunity to accumulate a substantial quantity of doppler noise data over a dynamic range of signal closest approach point heliographic latitudes. The observed doppler noise data were fit to the doppler noise model ISED, and the deviations of the observed doppler noise data from the model were used to construct a (multiplicative) function to describe the effect of heliographic latitude. This expression was then incorporated into the ISED model to produce a new doppler noise model-ISEDB.

Quantum Magnetism Applied to the Iron-Pnictides and Rare Earth Pyrochlores

NASA Astrophysics Data System (ADS)

Applegate, Ryan

This dissertation presents computational studies of two families of magnetic materials of significant current interest. The iron pnictides are new high temperature superconductors with interesting parent compound antiferromagnetism. The rare earth pyrochlore material Yb2Ti2O7 is a candidate quantum spin ice. The magnetic and structural phases of individual iron pnictides have both many common features and material specific differences. In an attempt to unify these behaviors as instances of a larger theoretical picture, we use Monte Carlo simulations of a two-dimensional Hamiltonian with coupled Heisenberg-spin and Ising-orbital degrees of freedom. We introduce spin-space and single-ion anisotropies and study the finite temperature transitions in our model. We develop a phase diagram and propose that the interplay of spin and orbital physics in the presence of anisotropy could explain how material details affect the transitions of the pnictide materials. Nuclear magnetic resonance (NMR) can study magnetic materials via the hyperfine interaction and the coupling between the nuclear moment and the field produced by the samples local moment environment. Recent measurements suggest that Zn doped BaFe2As2 may have quantum fluctuations about the striped phase that produce a distribution of fields at As nuclear sites. The non-magnetic ion Zn replaces Fe and can be treated as an impurity which can be studied by a zero-temperature Ising Series expansion method. We propose a Heisenberg-like J1a-J 1b-J2 model which has small ferromagnetic exchanges along the b axis and strong antiferromagnetic exchanges along the a axis. In our impurity model we find that the magnetic moments are everywhere reduced by quantum fluctuations, except on the nearest neighbor site in the AFM direction. We suggest that the presented impurity model may provide an explanation for the experimental measurements. Based on a recently proposed quantum spin ice model, we use numerical linked cluster (NLC) expansions to study thermodynamic properties of Yb 2Ti2O7. We show that high field fitting of inelastic neutron scattering experiments is an excellent method in determining the exchange constants of these materials. We calculate the heat capacity, entropy and magnetization as a function of temperature and field along a few high symmetry field directions. We compare our theoretical predictions to experiments and find remarkable agreement. These studies highlight the importance of localized model Hamiltonians in understanding magnetic properties of complex materials.

Sampling algorithms for validation of supervised learning models for Ising-like systems

NASA Astrophysics Data System (ADS)

Portman, Nataliya; Tamblyn, Isaac

2017-12-01

In this paper, we build and explore supervised learning models of ferromagnetic system behavior, using Monte-Carlo sampling of the spin configuration space generated by the 2D Ising model. Given the enormous size of the space of all possible Ising model realizations, the question arises as to how to choose a reasonable number of samples that will form physically meaningful and non-intersecting training and testing datasets. Here, we propose a sampling technique called ;ID-MH; that uses the Metropolis-Hastings algorithm creating Markov process across energy levels within the predefined configuration subspace. We show that application of this method retains phase transitions in both training and testing datasets and serves the purpose of validation of a machine learning algorithm. For larger lattice dimensions, ID-MH is not feasible as it requires knowledge of the complete configuration space. As such, we develop a new ;block-ID; sampling strategy: it decomposes the given structure into square blocks with lattice dimension N ≤ 5 and uses ID-MH sampling of candidate blocks. Further comparison of the performance of commonly used machine learning methods such as random forests, decision trees, k nearest neighbors and artificial neural networks shows that the PCA-based Decision Tree regressor is the most accurate predictor of magnetizations of the Ising model. For energies, however, the accuracy of prediction is not satisfactory, highlighting the need to consider more algorithmically complex methods (e.g., deep learning).

Self-avoiding walk on a square lattice with correlated vacancies

NASA Astrophysics Data System (ADS)

Cheraghalizadeh, J.; Najafi, M. N.; Mohammadzadeh, H.; Saber, A.

2018-04-01

The self-avoiding walk on the square site-diluted correlated percolation lattice is considered. The Ising model is employed to realize the spatial correlations of the metric space. As a well-accepted result, the (generalized) Flory's mean-field relation is tested to measure the effect of correlation. After exploring a perturbative Fokker-Planck-like equation, we apply an enriched Rosenbluth Monte Carlo method to study the problem. To be more precise, the winding angle analysis is also performed from which the diffusivity parameter of Schramm-Loewner evolution theory (κ ) is extracted. We find that at the critical Ising (host) system, the exponents are in agreement with Flory's approximation. For the off-critical Ising system, we find also a behavior for the fractal dimension of the walker trace in terms of the correlation length of the Ising system ξ (T ) , i.e., DFSAW(T ) -DFSAW(Tc) ˜1/√{ξ (T ) } .

An electric noise component with density 1/f identified on ISEE 3

NASA Technical Reports Server (NTRS)

Hoang, S.; Steinberg, J. L.; Couturier, P.; Feldman, W. C.

1982-01-01

The properties of the 1/f noise detected at the terminals of ISEE 3 antennas are described and related to the solar wind parameters. The 1/f noise was observed with the radio receivers of the three-dimensional radio mapping experiment using the S and Z dipole antennas. The noise spectra contained a negative spectral index component at frequencies lower than 0.7 of the plasma frequency, and 5-10 times the predicted thermal noise for the Z antenna. S-antenna measurements of the 1/f component revealed it to be deeply spin modulated with a minimum electric field in the direction of the solar wind. Modulation increases with increasing frequency, becomes negligible when the 1/f intensity is negligible with respect to the thermal noise, and increases with solar wind velocity. The possibilities that the noise is due either to waves or currents are discussed.

Quasiperiodic Quantum Ising Transitions in 1D

NASA Astrophysics Data System (ADS)

Crowley, P. J. D.; Chandran, A.; Laumann, C. R.

2018-04-01

Unlike random potentials, quasiperiodic modulation can induce localization-delocalization transitions in one dimension. In this Letter, we analyze the implications of this for symmetry breaking in the quasiperiodically modulated quantum Ising chain. Although weak modulation is irrelevant, strong modulation induces new ferromagnetic and paramagnetic phases which are fully localized and gapless. The quasiperiodic potential and localized excitations lead to quantum criticality that is intermediate to that of the clean and randomly disordered models with exponents of ν =1+ (exact) and z ≈1.9 , Δσ≈0.16 , and Δγ≈0.63 (up to logarithmic corrections). Technically, the clean Ising transition is destabilized by logarithmic wandering of the local reduced couplings. We conjecture that the wandering coefficient w controls the universality class of the quasiperiodic transition and show its stability to smooth perturbations that preserve the quasiperiodic structure of the model.

Critical phenomena on k -booklets

NASA Astrophysics Data System (ADS)

Grassberger, Peter

2017-01-01

We define a "k -booklet" to be a set of k semi-infinite planes with -∞

Ising model with conserved magnetization on the human connectome: Implications on the relation structure-function in wakefulness and anesthesia

NASA Astrophysics Data System (ADS)

Stramaglia, S.; Pellicoro, M.; Angelini, L.; Amico, E.; Aerts, H.; Cortés, J. M.; Laureys, S.; Marinazzo, D.

2017-04-01

Dynamical models implemented on the large scale architecture of the human brain may shed light on how a function arises from the underlying structure. This is the case notably for simple abstract models, such as the Ising model. We compare the spin correlations of the Ising model and the empirical functional brain correlations, both at the single link level and at the modular level, and show that their match increases at the modular level in anesthesia, in line with recent results and theories. Moreover, we show that at the peak of the specific heat (the critical state), the spin correlations are minimally shaped by the underlying structural network, explaining how the best match between the structure and function is obtained at the onset of criticality, as previously observed. These findings confirm that brain dynamics under anesthesia shows a departure from criticality and could open the way to novel perspectives when the conserved magnetization is interpreted in terms of a homeostatic principle imposed to neural activity.

Lifted worm algorithm for the Ising model

NASA Astrophysics Data System (ADS)

Elçi, Eren Metin; Grimm, Jens; Ding, Lijie; Nasrawi, Abrahim; Garoni, Timothy M.; Deng, Youjin

2018-04-01

We design an irreversible worm algorithm for the zero-field ferromagnetic Ising model by using the lifting technique. We study the dynamic critical behavior of an energylike observable on both the complete graph and toroidal grids, and compare our findings with reversible algorithms such as the Prokof'ev-Svistunov worm algorithm. Our results show that the lifted worm algorithm improves the dynamic exponent of the energylike observable on the complete graph and leads to a significant constant improvement on toroidal grids.

Condensation of helium in aerogel and athermal dynamics of the random-field Ising model.

PubMed

Aubry, Geoffroy J; Bonnet, Fabien; Melich, Mathieu; Guyon, Laurent; Spathis, Panayotis; Despetis, Florence; Wolf, Pierre-Etienne

2014-08-22

High resolution measurements reveal that condensation isotherms of (4)He in high porosity silica aerogel become discontinuous below a critical temperature. We show that this behavior does not correspond to an equilibrium phase transition modified by the disorder induced by the aerogel structure, but to the disorder-driven critical point predicted for the athermal out-of-equilibrium dynamics of the random-field Ising model. Our results evidence the key role of nonequilibrium effects in the phase transitions of disordered systems.

Frequency-Swept Integrated and Stretched Solid Effect Dynamic Nuclear Polarization.

PubMed

Can, T V; McKay, J E; Weber, R T; Yang, C; Dubroca, T; van Tol, J; Hill, S; Griffin, R G

2018-06-21

We investigate a new time domain approach to dynamic nuclear polarization (DNP), the frequency-swept integrated solid effect (FS-ISE), utilizing a high power, broadband 94 GHz (3.35 T) pulse EPR spectrometer. The bandwidth of the spectrometer enabled measurement of the DNP Zeeman frequency/field profile that revealed two dominant polarization mechanisms, the expected ISE, and a recently observed mechanism, the stretched solid effect (S 2 E). At 94 GHz, despite the limitations in the microwave chirp pulse length (10 μs) and the repetition rate (2 kHz), we obtained signal enhancements up to ∼70 for the S 2 E and ∼50 for the ISE. The results successfully demonstrate the viability of the FS-ISE and S 2 E DNP at a frequency 10 times higher than previous studies. Our results also suggest that these approaches are candidates for implementation at higher magnetic fields.

Two kinds of phase transitions in a voting model

NASA Astrophysics Data System (ADS)

Hisakado, M.; Mori, S.

2012-08-01

In this paper, we discuss a voting model with two candidates, C0 and C1. We consider two types of voters—herders and independents. The voting of independents is based on their fundamental values, while the voting of herders is based on the number of previous votes. We can identify two kinds of phase transitions. One is an information cascade transition similar to a phase transition seen in the Ising model. The other is a transition of super and normal diffusions. These phase transitions coexist. We compared our results to the conclusions of experiments and identified the phase transitions in the upper limit of the time t by using the analysis of human behavior obtained from experiments.

Universal scaling for the quantum Ising chain with a classical impurity

NASA Astrophysics Data System (ADS)

Apollaro, Tony J. G.; Francica, Gianluca; Giuliano, Domenico; Falcone, Giovanni; Palma, G. Massimo; Plastina, Francesco

2017-10-01

We study finite-size scaling for the magnetic observables of an impurity residing at the end point of an open quantum Ising chain with transverse magnetic field, realized by locally rescaling the field by a factor μ ≠1 . In the homogeneous chain limit at μ =1 , we find the expected finite-size scaling for the longitudinal impurity magnetization, with no specific scaling for the transverse magnetization. At variance, in the classical impurity limit μ =0 , we recover finite scaling for the longitudinal magnetization, while the transverse one basically does not scale. We provide both analytic approximate expressions for the magnetization and the susceptibility as well as numerical evidences for the scaling behavior. At intermediate values of μ , finite-size scaling is violated, and we provide a possible explanation of this result in terms of the appearance of a second, impurity-related length scale. Finally, by going along the standard quantum-to-classical mapping between statistical models, we derive the classical counterpart of the quantum Ising chain with an end-point impurity as a classical Ising model on a square lattice wrapped on a half-infinite cylinder, with the links along the first circle modified as a function of μ .

Discrepancies between implicit and explicit self-esteem among adolescents with social anxiety disorder.

PubMed

Schreiber, Franziska; Bohn, Christiane; Aderka, Idan M; Stangier, Ulrich; Steil, Regina

2012-12-01

Previous studies have found high implicit self-esteem (ISE) to prevail concurrently with low explicit self-esteem (ESE) in socially anxious adults. This suggests that self-esteem discrepancies are associated with social anxiety disorder (SAD). Given that the onset of SAD often occurs in adolescence, we investigated self-esteem discrepancies between ISE and ESE in adolescents suffering from SAD. Two implicit measures (Affect Misattribution Procedure, Implicit Association Test) were used both before and after a social threat activation in 20 adolescents with SAD (14-20 years), and compared to 20 healthy adolescents who were matched for age and gender. The Rosenberg Self-Esteem Scale, the Social Cognitions Questionnaire and Beck Depression Inventory were administered as explicit measures. We expected discrepant self-esteem (high ISE, low ESE) in adolescents with SAD, in comparison to congruent self-esteem (positive ISE, positive ESE) in healthy controls, after social threat activation. Both the patient and control groups exhibited high positive ISE on both implicit measures, before as well as after social threat induction. Explicitly, patients suffering from SAD revealed lower levels of ESE, compared to the healthy adolescents. This study is the first to examine ISE and ESE in a clinical sample of adolescent patients with SAD. Our results suggest that SAD is associated with a discrepancy between high ISE and low ESE, after a social-threat manipulation. The findings are discussed in relation to other studies using implicit measures in SAD and may provide a more comprehensive understanding of the role of self-esteem in adolescent SAD. Copyright © 2012 Elsevier Ltd. All rights reserved.

Experimental Mathematics and Mathematical Physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David

2009-06-26

One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.

Conformal perturbation of off-critical correlators in the 3D Ising universality class

NASA Astrophysics Data System (ADS)

Caselle, M.; Costagliola, G.; Magnoli, N.

2016-07-01

Thanks to the impressive progress of conformal bootstrap methods we have now very precise estimates of both scaling dimensions and operator product expansion coefficients for several 3D universality classes. We show how to use this information to obtain similarly precise estimates for off-critical correlators using conformal perturbation. We discuss in particular the ⟨σ (r )σ (0 )⟩ , ⟨ɛ (r )ɛ (0 )⟩ and ⟨σ (r )ɛ (0 )⟩ two-point functions in the high and low temperature regimes of the 3D Ising model and evaluate the leading and next to leading terms in the s =trΔt expansion, where t is the reduced temperature. Our results for ⟨σ (r )σ (0 )⟩ agree both with Monte Carlo simulations and with a set of experimental estimates of the critical scattering function.

Susceptibility of the Ising Model on a Kagomé Lattice by Using Wang-Landau Sampling

NASA Astrophysics Data System (ADS)

Kim, Seung-Yeon; Kwak, Wooseop

2018-03-01

The susceptibility of the Ising model on a kagomé lattice has never been obtained. We investigate the properties of the kagomé-lattice Ising model by using the Wang-Landau sampling method. We estimate both the magnetic scaling exponent yh = 1.90(1) and the thermal scaling exponent yt = 1.04(2) only from the susceptibility. From the estimated values of yh and yt, we obtain all the critical exponents, the specific-heat critical exponent α = 0.08(4), the spontaneous-magnetization critical exponent β = 0.10(1), the susceptibility critical exponent γ = 1.73(5), the isothermalmagnetization critical exponent δ = 16(4), the correlation-length critical exponent ν = 0.96(2), and the correlation-function critical exponent η = 0.20(4), without using any other thermodynamic function, such as the specific heat, magnetization, correlation length, and correlation function. One should note that the evaluation of all the critical exponents only from information on the susceptibility is an innovative approach.

Inferring network structure in non-normal and mixed discrete-continuous genomic data.

PubMed

Bhadra, Anindya; Rao, Arvind; Baladandayuthapani, Veerabhadran

2018-03-01

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional independence has been studied using sparse Gaussian graphical models for continuous data and sparse Ising models for discrete data. However, there are two clear situations when these approaches are inadequate. The first occurs when the data are continuous but display non-normal marginal behavior such as heavy tails or skewness, rendering an assumption of normality inappropriate. The second occurs when a part of the data is ordinal or discrete (e.g., presence or absence of a mutation) and the other part is continuous (e.g., expression levels of genes or proteins). In this case, the existing Bayesian approaches typically employ a latent variable framework for the discrete part that precludes inferring conditional independence among the data that are actually observed. The current article overcomes these two challenges in a unified framework using Gaussian scale mixtures. Our framework is able to handle continuous data that are not normal and data that are of mixed continuous and discrete nature, while still being able to infer a sparse conditional sign independence structure among the observed data. Extensive performance comparison in simulations with alternative techniques and an analysis of a real cancer genomics data set demonstrate the effectiveness of the proposed approach. © 2017, The International Biometric Society.

Inferring network structure in non-normal and mixed discrete-continuous genomic data

PubMed Central

Bhadra, Anindya; Rao, Arvind; Baladandayuthapani, Veerabhadran

2017-01-01

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional independence has been studied using sparse Gaussian graphical models for continuous data and sparse Ising models for discrete data. However, there are two clear situations when these approaches are inadequate. The first occurs when the data are continuous but display non-normal marginal behavior such as heavy tails or skewness, rendering an assumption of normality inappropriate. The second occurs when a part of the data is ordinal or discrete (e.g., presence or absence of a mutation) and the other part is continuous (e.g., expression levels of genes or proteins). In this case, the existing Bayesian approaches typically employ a latent variable framework for the discrete part that precludes inferring conditional independence among the data that are actually observed. The current article overcomes these two challenges in a unified framework using Gaussian scale mixtures. Our framework is able to handle continuous data that are not normal and data that are of mixed continuous and discrete nature, while still being able to infer a sparse conditional sign independence structure among the observed data. Extensive performance comparison in simulations with alternative techniques and an analysis of a real cancer genomics data set demonstrate the effectiveness of the proposed approach. PMID:28437848

Prospects of second generation artificial intelligence tools in calibration of chemical sensors.

PubMed

Braibanti, Antonio; Rao, Rupenaguntla Sambasiva; Ramam, Veluri Anantha; Rao, Gollapalli Nageswara; Rao, Vaddadi Venkata Panakala

2005-05-01

Multivariate data driven calibration models with neural networks (NNs) are developed for binary (Cu++ and Ca++) and quaternary (K+, Ca++, NO3- and Cl-) ion-selective electrode (ISE) data. The response profiles of ISEs with concentrations are non-linear and sub-Nernstian. This task represents function approximation of multi-variate, multi-response, correlated, non-linear data with unknown noise structure i.e. multi-component calibration/prediction in chemometric parlance. Radial distribution function (RBF) and Fuzzy-ARTMAP-NN models implemented in the software packages, TRAJAN and Professional II, are employed for the calibration. The optimum NN models reported are based on residuals in concentration space. Being a data driven information technology, NN does not require a model, prior- or posterior- distribution of data or noise structure. Missing information, spikes or newer trends in different concentration ranges can be modeled through novelty detection. Two simulated data sets generated from mathematical functions are modeled as a function of number of data points and network parameters like number of neurons and nearest neighbors. The success of RBF and Fuzzy-ARTMAP-NNs to develop adequate calibration models for experimental data and function approximation models for more complex simulated data sets ensures AI2 (artificial intelligence, 2nd generation) as a promising technology in quantitation.

Potentiometric detection of chemical vapors using molecularly imprinted polymers as receptors

PubMed Central

Liang, Rongning; Chen, Lusi; Qin, Wei

2015-01-01

Ion-selective electrode (ISE) based potentiometric gas sensors have shown to be promising analytical tools for detection of chemical vapors. However, such sensors are only capable of detecting those vapors which can be converted into ionic species in solution. This paper describes for the first time a polymer membrane ISE based potentiometric sensing system for sensitive and selective determination of neutral vapors in the gas phase. A molecularly imprinted polymer (MIP) is incorporated into the ISE membrane and used as the receptor for selective adsorption of the analyte vapor from the gas phase into the sensing membrane phase. An indicator ion with a structure similar to that of the vapor molecule is employed to indicate the change in the MIP binding sites in the membrane induced by the molecular recognition of the vapor. The toluene vapor is used as a model and benzoic acid is chosen as its indicator. Coupled to an apparatus manifold for preparation of vapor samples, the proposed ISE can be utilized to determine volatile toluene in the gas phase and allows potentiometric detection down to parts per million levels. This work demonstrates the possibility of developing a general sensing principle for detection of neutral vapors using ISEs. PMID:26215887

Implicit and Explicit Self-Esteem in Current, Remitted, Recovered, and Comorbid Depression and Anxiety Disorders: The NESDA Study

PubMed Central

van Tuijl, Lonneke A.; Glashouwer, Klaske A.; Bockting, Claudi L. H.; Tendeiro, Jorge N.; Penninx, Brenda W. J. H.; de Jong, Peter J.

2016-01-01

Background Dual processing models of psychopathology emphasize the relevance of differentiating between deliberative self-evaluative processes (explicit self-esteem; ESE) and automatically-elicited affective self-associations (implicit self-esteem; ISE). It has been proposed that both low ESE and ISE would be involved in major depressive disorder (MDD) and anxiety disorders (AD). Further, it has been hypothesized that MDD and AD may result in a low ISE “scar” that may contribute to recurrence after remission. However, the available evidence provides no straightforward support for the relevance of low ISE in MDD/AD, and studies testing the relevance of discrepant SE even showed that especially high ISE combined with low ESE is predictive of the development of internalizing symptoms. However, these earlier findings have been limited by small sample sizes, poorly defined groups in terms of comorbidity and phase of the disorders, and by using inadequate indices of discrepant SE. Therefore, this study tested further the proposed role of ISE and discrepant SE in a large-scale study allowing for stricter differentiation between groups and phase of disorder. Method In the context of the Netherlands Study of Depression and Anxiety (NESDA), we selected participants with current MDD (n = 60), AD (n = 111), and comorbid MDD/AD (n = 71), remitted MDD (n = 41), AD (n = 29), and comorbid MDD/AD (n = 14), recovered MDD (n = 136) and AD (n = 98), and never MDD or AD controls (n = 382). The Implicit Association Test was used to index ISE and the Rosenberg Self-Esteem Scale indexed ESE. Results Controls reported higher ESE than all other groups, and current comorbid MDD/AD had lower ESE than all other clinical groups. ISE was only lower than controls in current comorbid AD/MDD. Discrepant self-esteem (difference between ISE and ESE) was not associated with disorder status once controlling for ESE. Limitations Cross-sectional design limits causal inferences. Conclusion Findings suggest a prominent role for ESE in MDD and AD, while in comorbid MDD/AD negative self-evaluations are also present at the implicit level. There was no evidence to support the view that AD and MDD would result in a low ISE “scar”. PMID:27846292

Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice with interactions between next-to-nearest neighbors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Murtazaev, A. K.; Ramazanov, M. K., E-mail: sheikh77@mail.ru; Kassan-Ogly, F. A.

2015-01-15

Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice are studied on the basis of the replica algorithm by the Monte Carlo method and histogram analysis taking into account the interaction of next-to-nearest neighbors. The phase diagram of the dependence of the critical temperature on the intensity of interaction of the next-to-nearest neighbors is constructed. It is found that a second-order phase transition is realized in this model in the investigated interval of the intensities of interaction of next-to-nearest neighbors.

Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions

NASA Astrophysics Data System (ADS)

Gupta, Shamik

2017-10-01

In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we report on a very rich phase diagram in presence of thermal noise and an additional non-local interaction on a one-dimensional periodic lattice. Remarkably, the phase diagram involves both equilibrium and non-equilibrium phase transitions. In two contrasting limits of the dynamics, we obtain exact analytical results for the phase transitions. These two limits correspond to (i) the absence of thermal noise, when the dynamics reduces to that of a non-linear dynamical system, and (ii) the oscillators having the same natural frequency, when the dynamics becomes that of a statistical system in contact with a heat bath and relaxing to a statistical equilibrium state. In the former case, our exact analysis is based on the use of the so-called Ott-Antonsen ansatz to derive a reduced set of nonlinear partial differential equations for the macroscopic evolution of the system. Our results for the case of statistical equilibrium are on the other hand obtained by extending the well-known transfer matrix approach for nearest-neighbor Ising model to consider non-local interactions. The work offers a case study of exact analysis in many-body interacting systems. The results obtained underline the crucial role of additional non-local interactions in either destroying or enhancing the possibility of observing synchrony in mean-field systems exhibiting spontaneous synchronization.

Green Tea, Intermittent Sprinting Exercise, and Fat Oxidation

PubMed Central

Gahreman, Daniel; Wang, Rose; Boutcher, Yati; Boutcher, Stephen

2015-01-01

Fat oxidation has been shown to increase after short term green tea extract (GTE) ingestion and after one bout of intermittent sprinting exercise (ISE). Whether combining the two will result in greater fat oxidation after ISE is undetermined. The aim of the current study was to investigate the combined effect of short term GTE and a single session of ISE upon post-exercise fat oxidation. Fourteen women consumed three GTE or placebo capsules the day before and one capsule 90 min before a 20-min ISE cycling protocol followed by 1 h of resting recovery. Fat oxidation was calculated using indirect calorimetry. There was a significant increase in fat oxidation post-exercise compared to at rest in the placebo condition (p < 0.01). After GTE ingestion, however, at rest and post-exercise, fat oxidation was significantly greater (p < 0.05) than that after placebo. Plasma glycerol levels at rest and 15 min during post-exercise were significantly higher (p < 0.05) after GTE consumption compared to placebo. Compared to placebo, plasma catecholamines increased significantly after GTE consumption and 20 min after ISE (p < 0.05). Acute GTE ingestion significantly increased fat oxidation under resting and post-exercise conditions when compared to placebo. PMID:26184298

The influence of professional development on informal science educators' engagement of preschool-age audiences in science practices

NASA Astrophysics Data System (ADS)

Crowl, Michele

There is little research on professional development for informal science educators (ISEs). One particular area that ISEs need support in is how to engage preschool-age audiences in science practices. This study is part of a NSF-funded project, My Sky Tonight (MST), which looked at how to support ISEs in facilitating astronomy-themed activities with preschool-age audiences. This dissertation focuses on the influence of a six-week, online professional development workshop designed for ISEs working with preschool-age audiences. I used three primary sources of data: pre/post interviews and a video analysis task from data of 16 participants, as well as observations of implementation from a subset of seven participants who agreed to participate further. I developed and used the Phenomena-driven Practices of Science (PEPS) Framework as an analysis tool for identifying engagement in science practices. Findings from this study show that ISEs identified affective goals and rarely goals that reflect science practice engagement for their preschool-age audiences. They maintained these initial goals after the professional development workshop. ISEs describe the ways in which they engage children in science using primarily science practice-related words, but these descriptions did not show full use of science practices according to the PEPS framework. When observed implementing science activities with their preschool audiences, the ISEs demonstrated a variety of forms of science engagement, but only a few used science practices in ways consistent with the PEPS framework. Engagement in the professional development workshop did not result in a transition in the ways ISEs talk about and implement science with young children. While the write-ups for MST activities were not written in a way that supported engagement in science practices, a subset of MST activities were designed with it in mind. The professional development workshop included little time focusing on how ISEs could engage children in science practices, specific to each activity. These two factors may have played a major role in why participants showed limited improvement in their use of science practices in their goals and implementation.

La structure de Jordan des matrices de transfert des modeles de boucles et la relation avec les hamiltoniens XXZ

NASA Astrophysics Data System (ADS)

Morin-Duchesne, Alexi

Lattice models such as percolation, the Ising model and the Potts model are useful for the description of phase transitions in two dimensions. Finding analytical solutions is done by calculating the partition function, which in turn requires finding eigenvalues of transfer matrices. At the critical point, the two dimensional statistical models are invariant under conformal transformations and the construction of rational conformal field theories, as the continuum limit of these lattice models, allows one to compute the partition function at the critical point. Many researchers think however that the paradigm of rational conformal conformal field theories can be extended to include models with non diagonalizable transfer matrices. These models would then be described, in the scaling limit, by logarithmic conformal field theories and the representations of the Virasoro algebra coming into play would be indecomposable. We recall the construction of the double-row transfer matrix DN (λ, u) of the Fortuin-Kasteleyn model, seen as an element of the Temperley-Lieb algebra. This transfer matrix comes into play in physical theories through its representation in link modules (or standard modules). The vector space on which this representation acts decomposes into sectors labelled by a physical parameter d, the number of defects, which remains constant or decreases in the link representations. This thesis is devoted to the identification of the Jordan structure of DN(λ, u) in the link representations. The parameter β = 2 cos λ = -(q + q-1) fixes the theory : for instance β = 1 for percolation and 2 for the Ising model. On the geometry of the strip with open boundary conditions, we show that DN(λ, u) has the same Jordan blocks as its highest Fourier coefficient, FN. We study the non-diagonalizability of FN through the divergences of some of the eigenstates of ρ(F N) that appear at the critical values of λ. The Jordan cells we find in ρ(DN(λ, u)) have rank 2 and couple sectors d and d' when specific constraints on λ, d, d' and N are satisfied. For the model of critical dense polymers (β = 0) on the strip, the eigenvalues of ρ(DN(λ, u)) were known, but their degeneracies only conjectured. By constructing an isomorphism between the link modules on the strip and a subspace of spin modules of the XXZ model at q = i, we prove this conjecture. We also show that the restriction of the Hamiltonian to any sector d is diagonalizable, and that the XX Hamiltonian has rank 2 Jordan cells when N is even. Finally, we study the Jordan structure of the transfer matrix T N(λ, ν) for periodic boundary conditions. When λ = πa/b and a, b ∈ Z× , the matrix TN(λ, ν) has Jordan blocks between sectors, but also within sectors. The approach using FN admits a generalization to the present case and allows us to probe the Jordan cells that tie different sectors. The rank of these cells exceeds 2 in some cases and can grow indefinitely with N. For the Jordan blocks within a sector, we show that the link modules on the cylinder and the XXZ spin modules are isomorphic except for specific curves in the (q, ν) plane. By using the behavior of the transformation ĩd N in a neighborhood of the critical values (qc, ν c), we explicitly build Jordan partners of rank 2 and discuss the existence of Jordan cells with higher rank. Keywords : phase transitions, Ising model, Potts model, Fortuin-Kasteleyn model, transfer matrix method, XXZ Hamiltonian, logarithmic conformal field theory, Jordan structure.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anand, Nikhil; Genest, Vincent X.; Katz, Emanuel

We study 1+1 dimensional Φ 4 theory using the recently proposed method of conformal truncation. Starting in the UV CFT of free field theory, we construct a complete basis of states with definite conformal Casimir, C. We use these states to express the Hamiltonian of the full interacting theory in lightcone quantization. After truncating to states with C≤C max, we numerically diagonalize the Hamiltonian at strong coupling and study the resulting IR dynamics. We compute non-perturbative spectral densities of several local operators, which are equivalent to real-time, infinite-volume correlation functions. These spectral densities, which include the Zamolodchikov C-function along themore » full RG flow, are calculable at any value of the coupling. Near criticality, our numerical results reproduce correlation functions in the 2D Ising model.« less

Analysis and optimization of population annealing

NASA Astrophysics Data System (ADS)

Amey, Christopher; Machta, Jonathan

2018-03-01

Population annealing is an easily parallelizable sequential Monte Carlo algorithm that is well suited for simulating the equilibrium properties of systems with rough free-energy landscapes. In this work we seek to understand and improve the performance of population annealing. We derive several useful relations between quantities that describe the performance of population annealing and use these relations to suggest methods to optimize the algorithm. These optimization methods were tested by performing large-scale simulations of the three-dimensional (3D) Edwards-Anderson (Ising) spin glass and measuring several observables. The optimization methods were found to substantially decrease the amount of computational work necessary as compared to previously used, unoptimized versions of population annealing. We also obtain more accurate values of several important observables for the 3D Edwards-Anderson model.

Quantum annealing with all-to-all connected nonlinear oscillators

PubMed Central

Puri, Shruti; Andersen, Christian Kraglund; Grimsmo, Arne L.; Blais, Alexandre

2017-01-01

Quantum annealing aims at solving combinatorial optimization problems mapped to Ising interactions between quantum spins. Here, with the objective of developing a noise-resilient annealer, we propose a paradigm for quantum annealing with a scalable network of two-photon-driven Kerr-nonlinear resonators. Each resonator encodes an Ising spin in a robust degenerate subspace formed by two coherent states of opposite phases. A fully connected optimization problem is mapped to local fields driving the resonators, which are connected with only local four-body interactions. We describe an adiabatic annealing protocol in this system and analyse its performance in the presence of photon loss. Numerical simulations indicate substantial resilience to this noise channel, leading to a high success probability for quantum annealing. Finally, we propose a realistic circuit QED implementation of this promising platform for implementing a large-scale quantum Ising machine. PMID:28593952

Modeling in the Classroom: An Evolving Learning Tool

NASA Astrophysics Data System (ADS)

Few, A. A.; Marlino, M. R.; Low, R.

2006-12-01

Among the early programs (early 1990s) focused on teaching Earth System Science were the Global Change Instruction Program (GCIP) funded by NSF through UCAR and the Earth System Science Education Program (ESSE) funded by NASA through USRA. These two programs introduced modeling as a learning tool from the beginning, and they provided workshops, demonstrations and lectures for their participating universities. These programs were aimed at university-level education. Recently, classroom modeling is experiencing a revival of interest. Drs John Snow and Arthur Few conducted two workshops on modeling at the ESSE21 meeting in Fairbanks, Alaska, in August 2005. The Digital Library for Earth System Education (DLESE) at http://www.dlese.org provides web access to STELLA models and tutorials, and UCAR's Education and Outreach (EO) program holds workshops that include training in modeling. An important innovation to the STELLA modeling software by isee systems, http://www.iseesystems.com, called "isee Player" is available as a free download. The Player allows users to view and run STELLA models, change model parameters, share models with colleagues and students, and make working models available on the web. This is important because the expert can create models, and the user can learn how the modeled system works. Another aspect of this innovation is that the educational benefits of modeling concepts can be extended throughout most of the curriculum. The procedure for building a working computer model of an Earth Science System follows this general format: (1) carefully define the question(s) for which you seek the answer(s); (2) identify the interacting system components and inputs contributing to the system's behavior; (3) collect the information and data that will be required to complete the conceptual model; (4) construct a system diagram (graphic) of the system that displays all of system's central questions, components, relationships and required inputs. At this stage in the process the conceptual model of the system is compete and a clear understanding of how the system works is achieved. When appropriate software is available the advanced classes can proceed to (5) creating a computer model of the system and testing the conceptual model. For classes lacking these advanced capabilities they may view and run models using the free isee Player and shared working models. In any event there is understanding to be gained in every step of the procedure outlined above. You can view some examples at http://www.ruf.rice.edu/~few/. We plan to populate this site with samples of Earth science systems for use in Earth system science education.

Frequency-dependent dynamic magnetic properties of the Ising bilayer system consisting of spin-3/2 and spin-5/2 spins

NASA Astrophysics Data System (ADS)

Keskin, Mustafa; Ertaş, Mehmet

2018-04-01

Dynamic magnetic properties of the Ising bilayer system consisting of the mixed (3/2, 5/2) Ising spins with a crystal-field interaction in an oscillating field on a two-layer square lattice is studied by the use of dynamic mean-field theory based on the Glauber-type stochastic. Dynamic phase transition temperatures are obtained and dynamic phase diagrams are presented in three different planes. The frequency dependence of dynamic hysteresis loops is also investigated in detail. We compare the results with some available theoretical and experimental works and observe a quantitatively good agreement with some theoretical and experimental results.

Error threshold for color codes and random three-body Ising models.

PubMed

Katzgraber, Helmut G; Bombin, H; Martin-Delgado, M A

2009-08-28

We study the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates suitable for entanglement distillation, teleportation, and fault-tolerant quantum computation. We map the error-correction process onto a statistical mechanical random three-body Ising model and study its phase diagram via Monte Carlo simulations. The obtained error threshold of p(c) = 0.109(2) is very close to that of Kitaev's toric code, showing that enhanced computational capabilities do not necessarily imply lower resistance to noise.

Monte Carlo technique for very large ising models

NASA Astrophysics Data System (ADS)

Kalle, C.; Winkelmann, V.

1982-08-01

Rebbi's multispin coding technique is improved and applied to the kinetic Ising model with size 600*600*600. We give the central part of our computer program (for a CDC Cyber 76), which will be helpful also in a simulation of smaller systems, and describe the other tricks necessary to go to large lattices. The magnetization M at T=1.4* T c is found to decay asymptotically as exp(-t/2.90) if t is measured in Monte Carlo steps per spin, and M( t = 0) = 1 initially.