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.

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).

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 .

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.

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

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.

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

NASA Astrophysics Data System (ADS)

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 Tc 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 DfSAW=4/3 . Also, the corresponding open curves has conformal invariance with the root-mean-square distance Rrms˜t3 /4 (t being the parametrization of the curve) in accordance with the 2D SAW. In the finite-size study, we observe that at T =Tc 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 =Tc . In the off-critical temperatures in the close vicinity of Tc the exponents show some additional power-law behaviors in terms of T -Tc with some exponents that are reported in the text. The spanning cluster probability at the critical temperature also scales with L1/2, which is different from the regular 2D BTW model.

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.

Ashkin-Teller criticality and weak first-order behavior of the phase transition to a fourfold degenerate state in two-dimensional frustrated Ising antiferromagnets

NASA Astrophysics Data System (ADS)

Liu, R. M.; Zhuo, W. Z.; Chen, J.; Qin, M. H.; Zeng, M.; Lu, X. B.; Gao, X. S.; Liu, J.-M.

2017-07-01

We study the thermal phase transition of the fourfold degenerate phases (the plaquette and single-stripe states) in the two-dimensional frustrated Ising model on the Shastry-Sutherland lattice using Monte Carlo simulations. The critical Ashkin-Teller-like behavior is identified both in the plaquette phase region and the single-stripe phase region. The four-state Potts critical end points differentiating the continuous transitions from the first-order ones are estimated based on finite-size-scaling analyses. Furthermore, a similar behavior of the transition to the fourfold single-stripe phase is also observed in the anisotropic triangular Ising model. Thus, this work clearly demonstrates that the transitions to the fourfold degenerate states of two-dimensional Ising antiferromagnets exhibit similar transition behavior.

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

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).

From Cycle Rooted Spanning Forests to the Critical Ising Model: an Explicit Construction

NASA Astrophysics Data System (ADS)

de Tilière, Béatrice

2013-04-01

Fisher established an explicit correspondence between the 2-dimensional Ising model defined on a graph G and the dimer model defined on a decorated version {{G}} of this graph (Fisher in J Math Phys 7:1776-1781, 1966). In this paper we explicitly relate the dimer model associated to the critical Ising model and critical cycle rooted spanning forests (CRSFs). This relation is established through characteristic polynomials, whose definition only depends on the respective fundamental domains, and which encode the combinatorics of the model. We first show a matrix-tree type theorem establishing that the dimer characteristic polynomial counts CRSFs of the decorated fundamental domain {{G}_1}. Our main result consists in explicitly constructing CRSFs of {{G}_1} counted by the dimer characteristic polynomial, from CRSFs of G 1, where edges are assigned Kenyon's critical weight function (Kenyon in Invent Math 150(2):409-439, 2002); thus proving a relation on the level of configurations between two well known 2-dimensional critical models.

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.

Phase transitions and thermodynamic properties of antiferromagnetic Ising model with next-nearest-neighbor interactions on the Kagomé lattice

NASA Astrophysics Data System (ADS)

Ramazanov, M. K.; Murtazaev, A. K.; Magomedov, M. A.; Badiev, M. K.

2018-06-01

We study phase transitions and thermodynamic properties in the two-dimensional antiferromagnetic Ising model with next-nearest-neighbor interaction on a Kagomé lattice by Monte Carlo simulations. A histogram data analysis shows that a second-order transition occurs in the model. From the analysis of obtained data, we can assume that next-nearest-neighbor ferromagnetic interactions in two-dimensional antiferromagnetic Ising model on a Kagomé lattice excite the occurrence of a second-order transition and unusual behavior of thermodynamic properties on the temperature dependence.

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.

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.

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.

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.

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.

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).

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.

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].

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.

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.

Chaotic Ising-like dynamics in traffic signals

PubMed Central

Suzuki, Hideyuki; Imura, Jun-ichi; Aihara, Kazuyuki

2013-01-01

The green and red lights of a traffic signal can be viewed as the up and down states of an Ising spin. Moreover, traffic signals in a city interact with each other, if they are controlled in a decentralised way. In this paper, a simple model of such interacting signals on a finite-size two-dimensional lattice is shown to have Ising-like dynamics that undergoes a ferromagnetic phase transition. Probabilistic behaviour of the model is realised by chaotic billiard dynamics that arises from coupled non-chaotic elements. This purely deterministic model is expected to serve as a starting point for considering statistical mechanics of traffic signals. PMID:23350034

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

Spreadsheet analysis of stability and meta-stability of low-dimensional magnetic particles using the Ising approach

NASA Astrophysics Data System (ADS)

Ehrmann, Andrea; Blachowicz, Tomasz; Zghidi, Hafed

2015-05-01

Modelling hysteresis behaviour, as it can be found in a broad variety of dynamical systems, can be performed in different ways. An elementary approach, applied for a set of elementary cells, which uses only two possible states per cell, is the Ising model. While such Ising models allow for a simulation of many systems with sufficient accuracy, they nevertheless depict some typical features which must be taken into account with proper care, such as meta-stability or the externally applied field sweeping speed. This paper gives a general overview of recent results from Ising models from the perspective of a didactic model, based on a 2D spreadsheet analysis, which can be used also for solving general scientific problems where direct next-neighbour interactions take place.

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

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.

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

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.

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.

Interacting damage models mapped onto ising and percolation models

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

Toussaint, Renaud; Pride, Steven R.

The authors introduce a class of damage models on regular lattices with isotropic interactions between the broken cells of the lattice. Quasistatic fiber bundles are an example. The interactions are assumed to be weak, in the sense that the stress perturbation from a broken cell is much smaller than the mean stress in the system. The system starts intact with a surface-energy threshold required to break any cell sampled from an uncorrelated quenched-disorder distribution. The evolution of this heterogeneous system is ruled by Griffith's principle which states that a cell breaks when the release in potential (elastic) energy in themore » system exceeds the surface-energy barrier necessary to break the cell. By direct integration over all possible realizations of the quenched disorder, they obtain the probability distribution of each damage configuration at any level of the imposed external deformation. They demonstrate an isomorphism between the distributions so obtained and standard generalized Ising models, in which the coupling constants and effective temperature in the Ising model are functions of the nature of the quenched-disorder distribution and the extent of accumulated damage. In particular, they show that damage models with global load sharing are isomorphic to standard percolation theory, that damage models with local load sharing rule are isomorphic to the standard ising model, and draw consequences thereof for the universality class and behavior of the autocorrelation length of the breakdown transitions corresponding to these models. they also treat damage models having more general power-law interactions, and classify the breakdown process as a function of the power-law interaction exponent. Last, they also show that the probability distribution over configurations is a maximum of Shannon's entropy under some specific constraints related to the energetic balance of the fracture process, which firmly relates this type of quenched-disorder based

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

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.

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.

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

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.

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.

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.

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.

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.

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

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…

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.

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.

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.

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.

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.

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.

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.

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.

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].

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.

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.

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.

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.

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.

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.

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

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.

Configuration memory in patchwork dynamics for low-dimensional spin glasses

NASA Astrophysics Data System (ADS)

Yang, Jie; Middleton, A. Alan

2017-12-01

A patchwork method is used to study the dynamics of loss and recovery of an initial configuration in spin glass models in dimensions d =1 and d =2 . The patchwork heuristic is used to accelerate the dynamics to investigate how models might reproduce the remarkable memory effects seen in experiment. Starting from a ground-state configuration computed for one choice of nearest-neighbor spin couplings, the sample is aged up to a given scale under new random couplings, leading to the partial erasure of the original ground state. The couplings are then restored to the original choice and patchwork coarsening is again applied, in order to assess the recovery of the original state. Eventual recovery of the original ground state upon coarsening is seen in two-dimensional Ising spin glasses and one-dimensional clock models, while one-dimensional Ising spin systems neither lose nor gain overlap with the ground state during the recovery stage. The recovery for the two-dimensional Ising spin glasses suggests scaling relations that lead to a recovery length scale that grows as a power of the aging length scale.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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).

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.

ISE structural dynamic experiments

NASA Technical Reports Server (NTRS)

Lock, Malcolm H.; Clark, S. Y.

1988-01-01

The topics are presented in viewgraph form and include the following: directed energy systems - vibration issue; Neutral Particle Beam Integrated Space Experiment (NPB-ISE) opportunity/study objective; vibration sources/study plan; NPB-ISE spacecraft configuration; baseline slew analysis and results; modal contributions; fundamental pitch mode; vibration reduction approaches; peak residual vibration; NPB-ISE spacecraft slew experiment; goodbye ISE - hello Zenith Star Program.

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.

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.

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.

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).

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.

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.

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.

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.

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.

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).

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.

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

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.

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.

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.

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.

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.

Simulation of financial market via nonlinear Ising model

NASA Astrophysics Data System (ADS)

Ko, Bonggyun; Song, Jae Wook; Chang, Woojin

2016-09-01

In this research, we propose a practical method for simulating the financial return series whose distribution has a specific heaviness. We employ the Ising model for generating financial return series to be analogous to those of the real series. The similarity between real financial return series and simulated one is statistically verified based on their stylized facts including the power law behavior of tail distribution. We also suggest the scheme for setting the parameters in order to simulate the financial return series with specific tail behavior. The simulation method introduced in this paper is expected to be applied to the other financial products whose price return distribution is fat-tailed.

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].

Stochastic bifurcations in the nonlinear parallel Ising model.

PubMed

Bagnoli, Franco; Rechtman, Raúl

2016-11-01

We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.

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.

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).

Renormalization group, normal form theory and the Ising model

NASA Astrophysics Data System (ADS)

Raju, Archishman; Hayden, Lorien; Clement, Colin; Liarte, Danilo; Sethna, James

The results of the renormalization group are commonly advertised as the existence of power law singularities at critical points. Logarithmic and exponential corrections are seen as special cases and dealt with on a case-by-case basis. We propose to systematize computing the singularities in the renormalization group using perturbative normal form theory. This gives us a way to classify all such singularities in a unified framework and to generate a systematic machinery to do scaling collapses. We show that this procedure leads to some new results even in classic cases like the Ising model and has general applicability.

Nuclear and ionic charge distribution experiment on ISEE-1 and ISEE-3

NASA Technical Reports Server (NTRS)

Gloeckler, G.; Ipavich, F. M.; Galvin, A. B.

1987-01-01

The experimental work carried out under this contract is a continuation of that originally performed under Contracts NAS5-20062 and NAS5-26739. The data analyzed are from the Max-Planck Institut/Univ. of Maryland experiment on ISEE-1 and ISEE-3. Each spacecraft experiment consists of a nearly identical set of three sensors (designated the ULECA, ULEWAT, and ULEZEQ sensors) designed to measure the energy spectra and composition of suprathermal and energetic ions over a broad energy range (less than 3 keV/e to more than 20 MeV/nucleon). Since the launch of ISEE's 2 and 3, the MPI/Univ. of Maryland experiments have generally performed as expected except for a partial failure of the ULEWAT sensor on ISEE-1 in August 1978. A number of scientific studies have either been completed, initiated or are at various stages of completion. A brief summary of Primary Results is given, followed by a more detailed summary of the major accomplishments at the Univ. of Maryland.

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.

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.

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.

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.

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.

Modelling sodium cobaltate by mapping onto magnetic Ising model

NASA Astrophysics Data System (ADS)

Gemperline, Patrick; Morris, David Jonathan Pryce

Fast Ion conductors are a class of crystals that are frequently used as battery materials, especially in smart phones, laptops, and other portable devices. Sodium Cobalt Oxide, NaxCoO2, falls into this class of crystals, but is unique because it possesses the ability to act as a thermoelectric material and a superconductor at different concentrations of Na+. The crystal lattice is mapped onto an Ising Magnetic Spin model and a Monte-Carol Simulation is used to find the most energetically favorable configuration of spins. This spin configuration is mapped back to the crystal lattice resulting in the most stable crystal structure of Sodium Cobalt Oxide at various concentrations. Knowing the atomic structures of the crystals will aid in the research of the materials capabilities and the possible uses of the material commercially. Ohio Supercomputer Center. 1987. Ohio Supercomputer Center. Columbus OH: Ohio Supercomputer Center. and the John Hauck Foundation.

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.

Ising formulation of associative memory models and quantum annealing recall

NASA Astrophysics Data System (ADS)

Santra, Siddhartha; Shehab, Omar; Balu, Radhakrishnan

2017-12-01

Associative memory models, in theoretical neuro- and computer sciences, can generally store at most a linear number of memories. Recalling memories in these models can be understood as retrieval of the energy minimizing configuration of classical Ising spins, closest in Hamming distance to an imperfect input memory, where the energy landscape is determined by the set of stored memories. We present an Ising formulation for associative memory models and consider the problem of memory recall using quantum annealing. We show that allowing for input-dependent energy landscapes allows storage of up to an exponential number of memories (in terms of the number of neurons). Further, we show how quantum annealing may naturally be used for recall tasks in such input-dependent energy landscapes, although the recall time may increase with the number of stored memories. Theoretically, we obtain the radius of attractor basins R (N ) and the capacity C (N ) of such a scheme and their tradeoffs. Our calculations establish that for randomly chosen memories the capacity of our model using the Hebbian learning rule as a function of problem size can be expressed as C (N ) =O (eC1N) , C1≥0 , and succeeds on randomly chosen memory sets with a probability of (1 -e-C2N) , C2≥0 with C1+C2=(0.5-f ) 2/(1 -f ) , where f =R (N )/N , 0 ≤f ≤0.5 , is the radius of attraction in terms of the Hamming distance of an input probe from a stored memory as a fraction of the problem size. We demonstrate the application of this scheme on a programmable quantum annealing device, the D-wave processor.

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.

ISE: An Integrated Search Environment. The manual

NASA Technical Reports Server (NTRS)

Chu, Lon-Chan

1992-01-01

Integrated Search Environment (ISE), a software package that implements hierarchical searches with meta-control, is described in this manual. ISE is a collection of problem-independent routines to support solving searches. Mainly, these routines are core routines for solving a search problem and they handle the control of searches and maintain the statistics related to searches. By separating the problem-dependent and problem-independent components in ISE, new search methods based on a combination of existing methods can be developed by coding a single master control program. Further, new applications solved by searches can be developed by coding the problem-dependent parts and reusing the problem-independent parts already developed. Potential users of ISE are designers of new application solvers and new search algorithms, and users of experimental application solvers and search algorithms. The ISE is designed to be user-friendly and information rich. In this manual, the organization of ISE is described and several experiments carried out on ISE are also described.

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.

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.

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.

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.

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.

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.

Cavity master equation for the continuous time dynamics of discrete-spin models.

PubMed

Aurell, E; Del Ferraro, G; Domínguez, E; Mulet, R

2017-05-01

We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of the theory of random point processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean-field ferromagnet and the dynamics of the one-dimensional Ising system. We present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the random field Ising model, and the Viana-Bray spin-glass model.

Cavity master equation for the continuous time dynamics of discrete-spin models

NASA Astrophysics Data System (ADS)

Aurell, E.; Del Ferraro, G.; Domínguez, E.; Mulet, R.

2017-05-01

We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of the theory of random point processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean-field ferromagnet and the dynamics of the one-dimensional Ising system. We present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the random field Ising model, and the Viana-Bray spin-glass model.

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.

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.

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.

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.

OpenCL Implementation of NeuroIsing

NASA Astrophysics Data System (ADS)

Zapart, C. A.

Recent advances in graphics card hardware combined with anintroduction of the OpenCL standard promise to accelerate numerical simulations across diverse scientific disciplines. One such field benefiting from new hardware/software paradigms is econophysics. The paper describes an OpenCL implementation of a selected econophysics model: NeuroIsing, which has been designed to execute in parallel on a vendor-independent graphics card. Originally introduced in the paper [C.~A.~Zapart, ``Econophysics in Financial Time Series Prediction'', PhD thesis, Graduate University for Advanced Studies, Japan (2009)], at first it was implemented on a CELL processor running inside a SONY PS3 games console. The NeuroIsing framework can be applied to predicting and trading foreign exchange as well as stock market index futures.

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.

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.

Long-range Ising model for credit portfolios with heterogeneous credit exposures

NASA Astrophysics Data System (ADS)

Kato, Kensuke

2016-11-01

We propose the finite-size long-range Ising model as a model for heterogeneous credit portfolios held by a financial institution in the view of econophysics. The model expresses the heterogeneity of the default probability and the default correlation by dividing a credit portfolio into multiple sectors characterized by credit rating and industry. The model also expresses the heterogeneity of the credit exposure, which is difficult to evaluate analytically, by applying the replica exchange Monte Carlo method to numerically calculate the loss distribution. To analyze the characteristics of the loss distribution for credit portfolios with heterogeneous credit exposures, we apply this model to various credit portfolios and evaluate credit risk. As a result, we show that the tail of the loss distribution calculated by this model has characteristics that are different from the tail of the loss distribution of the standard models used in credit risk modeling. We also show that there is a possibility of different evaluations of credit risk according to the pattern of heterogeneity.

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 .

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.

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.

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.

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.

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.

92 Years of the Ising Model: A High Resolution Monte Carlo Study

NASA Astrophysics Data System (ADS)

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

2018-04-01

Using extensive Monte Carlo simulations that employ the Wolff cluster flipping 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, we obtained the critical inverse temperature K c = 0.221 654 626(5) and the critical exponent of the correlation length ν = 0.629 912(86) with precision that improves upon previous Monte Carlo estimates.

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.

Evaluation of tranche in securitization and long-range Ising model

NASA Astrophysics Data System (ADS)

Kitsukawa, K.; Mori, S.; Hisakado, M.

2006-08-01

This econophysics work studies the long-range Ising model of a finite system with N spins and the exchange interaction J/N and the external field H as a model for homogeneous credit portfolio of assets with default probability Pd and default correlation ρd. Based on the discussion on the (J,H) phase diagram, we develop a perturbative calculation method for the model and obtain explicit expressions for Pd,ρd and the normalization factor Z in terms of the model parameters N and J,H. The effect of the default correlation ρd on the probabilities P(Nd,ρd) for Nd defaults and on the cumulative distribution function D(i,ρd) are discussed. The latter means the average loss rate of the“tranche” (layered structure) of the securities (e.g. CDO), which are synthesized from a pool of many assets. We show that the expected loss rate of the subordinated tranche decreases with ρd and that of the senior tranche increases linearly, which are important in their pricing and ratings.

Learning and inference in a nonequilibrium Ising model with hidden nodes.

PubMed

Dunn, Benjamin; Roudi, Yasser

2013-02-01

We study inference and reconstruction of couplings in a partially observed kinetic Ising model. With hidden spins, calculating the likelihood of a sequence of observed spin configurations requires performing a trace over the configurations of the hidden ones. This, as we show, can be represented as a path integral. Using this representation, we demonstrate that systematic approximate inference and learning rules can be derived using dynamical mean-field theory. Although naive mean-field theory leads to an unstable learning rule, taking into account Gaussian corrections allows learning the couplings involving hidden nodes. It also improves learning of the couplings between the observed nodes compared to when hidden nodes are ignored.

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.

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.

Quasi-additive estimates on the Hamiltonian for the one-dimensional long range Ising model

NASA Astrophysics Data System (ADS)

Littin, Jorge; Picco, Pierre

2017-07-01

In this work, we study the problem of getting quasi-additive bounds for the Hamiltonian of the long range Ising model, when the two-body interaction term decays proportionally to 1/d2 -α , α ∈(0,1 ) . We revisit the paper by Cassandro et al. [J. Math. Phys. 46, 053305 (2005)] where they extend to the case α ∈[0 ,ln3/ln2 -1 ) the result of the existence of a phase transition by using a Peierls argument given by Fröhlich and Spencer [Commun. Math. Phys. 84, 87-101 (1982)] for α =0 . The main arguments of Cassandro et al. [J. Math. Phys. 46, 053305 (2005)] are based in a quasi-additive decomposition of the Hamiltonian in terms of hierarchical structures called triangles and contours, which are related to the original definition of contours introduced by Fröhlich and Spencer [Commun. Math. Phys. 84, 87-101 (1982)]. In this work, we study the existence of a quasi-additive decomposition of the Hamiltonian in terms of the contours defined in the work of Cassandro et al. [J. Math. Phys. 46, 053305 (2005)]. The most relevant result obtained is Theorem 4.3 where we show that there is a quasi-additive decomposition for the Hamiltonian in terms of contours when α ∈[0,1 ) but not in terms of triangles. The fact that it cannot be a quasi-additive bound in terms of triangles lead to a very interesting maximization problem whose maximizer is related to a discrete Cantor set. As a consequence of the quasi-additive bounds, we prove that we can generalise the [Cassandro et al., J. Math. Phys. 46, 053305 (2005)] result, that is, a Peierls argument, to the whole interval α ∈[0,1 ) . We also state here the result of Cassandro et al. [Commun. Math. Phys. 327, 951-991 (2014)] about cluster expansions which implies that Theorem 2.4 that concerns interfaces and Theorem 2.5 that concerns n point truncated correlation functions in Cassandro et al. [Commun. Math. Phys. 327, 951-991 (2014)] are valid for all α ∈[0,1 ) instead of only α ∈[0 ,ln3/ln2 -1 ) .

AIM for Allostery: Using the Ising Model to Understand Information Processing and Transmission in Allosteric Biomolecular Systems.

PubMed

LeVine, Michael V; Weinstein, Harel

2015-05-01

In performing their biological functions, molecular machines must process and transmit information with high fidelity. Information transmission requires dynamic coupling between the conformations of discrete structural components within the protein positioned far from one another on the molecular scale. This type of biomolecular "action at a distance" is termed allostery . Although allostery is ubiquitous in biological regulation and signal transduction, its treatment in theoretical models has mostly eschewed quantitative descriptions involving the system's underlying structural components and their interactions. Here, we show how Ising models can be used to formulate an approach to allostery in a structural context of interactions between the constitutive components by building simple allosteric constructs we termed Allosteric Ising Models (AIMs). We introduce the use of AIMs in analytical and numerical calculations that relate thermodynamic descriptions of allostery to the structural context, and then show that many fundamental properties of allostery, such as the multiplicative property of parallel allosteric channels, are revealed from the analysis of such models. The power of exploring mechanistic structural models of allosteric function in more complex systems by using AIMs is demonstrated by building a model of allosteric signaling for an experimentally well-characterized asymmetric homodimer of the dopamine D2 receptor.

Modeling Dark Energy Through AN Ising Fluid with Network Interactions

NASA Astrophysics Data System (ADS)

Luongo, Orlando; Tommasini, Damiano

2014-12-01

We show that the dark energy (DE) effects can be modeled by using an Ising perfect fluid with network interactions, whose low redshift equation of state (EoS), i.e. ω0, becomes ω0 = -1 as in the ΛCDM model. In our picture, DE is characterized by a barotropic fluid on a lattice in the equilibrium configuration. Thus, mimicking the spin interaction by replacing the spin variable with an occupational number, the pressure naturally becomes negative. We find that the corresponding EoS mimics the effects of a variable DE term, whose limiting case reduces to the cosmological constant Λ. This permits us to avoid the introduction of a vacuum energy as DE source by hand, alleviating the coincidence and fine tuning problems. We find fairly good cosmological constraints, by performing three tests with supernovae Ia (SNeIa), baryonic acoustic oscillation (BAO) and cosmic microwave background (CMB) measurements. Finally, we perform the Akaike information criterion (AIC) and Bayesian information criterion (BIC) selection criteria, showing that our model is statistically favored with respect to the Chevallier-Polarsky-Linder (CPL) parametrization.

Transverse fields to tune an Ising-nematic quantum phase transition [Transverse fields to tune an Ising-nematic quantum critical transition

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

Maharaj, Akash V.; Rosenberg, Elliott W.; Hristov, Alexander T.

Here, the paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a quantum phase transition also depends on the dynamics. In the transverse field Ising model, the order parameter is not conserved, and increasing the transverse field enhances quantum fluctuations until they become strong enough to restore the symmetry of the ground state. Ising pseudospins can represent the order parameter of any system with a twofold degenerate broken-symmetry phase, including electronic nematic order associated withmore » spontaneous point-group symmetry breaking. Here, we show for the representative example of orbital-nematic ordering of a non-Kramers doublet that an orthogonal strain or a perpendicular magnetic field plays the role of the transverse field, thereby providing a practical route for tuning appropriate materials to a quantum critical point. While the transverse fields are conjugate to seemingly unrelated order parameters, their nontrivial commutation relations with the nematic order parameter, which can be represented by a Berry-phase term in an effective field theory, intrinsically intertwine the different order parameters.« less

Transverse fields to tune an Ising-nematic quantum phase transition [Transverse fields to tune an Ising-nematic quantum critical transition

DOE PAGES

Maharaj, Akash V.; Rosenberg, Elliott W.; Hristov, Alexander T.; ...

2017-12-05

Here, the paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a quantum phase transition also depends on the dynamics. In the transverse field Ising model, the order parameter is not conserved, and increasing the transverse field enhances quantum fluctuations until they become strong enough to restore the symmetry of the ground state. Ising pseudospins can represent the order parameter of any system with a twofold degenerate broken-symmetry phase, including electronic nematic order associated withmore » spontaneous point-group symmetry breaking. Here, we show for the representative example of orbital-nematic ordering of a non-Kramers doublet that an orthogonal strain or a perpendicular magnetic field plays the role of the transverse field, thereby providing a practical route for tuning appropriate materials to a quantum critical point. While the transverse fields are conjugate to seemingly unrelated order parameters, their nontrivial commutation relations with the nematic order parameter, which can be represented by a Berry-phase term in an effective field theory, intrinsically intertwine the different order parameters.« less

The critical 1-arm exponent for the ferromagnetic Ising model on the Bethe lattice

NASA Astrophysics Data System (ADS)

Heydenreich, Markus; Kolesnikov, Leonid

2018-04-01

We consider the ferromagnetic nearest-neighbor Ising model on regular trees (Bethe lattice), which is well-known to undergo a phase transition in the absence of an external magnetic field. The behavior of the model at critical temperature can be described in terms of various critical exponents; one of them is the critical 1-arm exponent ρ which characterizes the rate of decay of the (root) magnetization as a function of the distance to the boundary. The crucial quantity we analyze in this work is the thermal expectation of the root spin on a finite subtree, where the expected value is taken with respect to a probability measure related to the corresponding finite-volume Hamiltonian with a fixed boundary condition. The spontaneous magnetization, which is the limit of this thermal expectation in the distance between the root and the boundary (i.e., in the height of the subtree), is known to vanish at criticality. We are interested in a quantitative analysis of the rate of this convergence in terms of the critical 1-arm exponent ρ. Therefore, we rigorously prove that ⟨σ0⟩ n +, the thermal expectation of the root spin at the critical temperature and in the presence of the positive boundary condition, decays as ⟨σ0 ⟩ n +≈n-1/2 (in a rather sharp sense), where n is the height of the tree. This establishes the 1-arm critical exponent for the Ising model on regular trees (ρ =1/2 ).

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.

Robust criticality of an Ising model on rewired directed networks

NASA Astrophysics Data System (ADS)

Lipowski, Adam; Gontarek, Krzysztof; Lipowska, Dorota

2015-06-01

We show that preferential rewiring, which is supposed to mimic the behavior of financial agents, changes a directed-network Ising ferromagnet with a single critical point into a model with robust critical behavior. For the nonrewired random graph version, due to a constant number of out-links for each site, we write a simple mean-field-like equation describing the behavior of magnetization; we argue that it is exact and support the claim with extensive Monte Carlo simulations. For the rewired version, this equation is obeyed only at low temperatures. At higher temperatures, rewiring leads to strong heterogeneities, which apparently invalidates mean-field arguments and induces large fluctuations and divergent susceptibility. Such behavior is traced back to the formation of a relatively small core of agents that influence the entire system.

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.

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.

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.

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.

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.

Ising-like patterns of spatial synchrony in population biology

NASA Astrophysics Data System (ADS)

Noble, Andrew; Hastings, Alan; Machta, Jon

2014-03-01

Systems of coupled dynamical oscillators can undergo a phase transition between synchronous and asynchronous phases. In the case of coupled map lattices, the spontaneous symmetry breaking of a temporal-phase order parameter is known to exhibit Ising-like critical behavior. Here, we investigate a noisy coupled map motivated by the study of spatial synchrony in ecological populations far from the extinction threshold. Ising-like patterns of criticality, as well as spinodal decomposition and homogeneous nucleation, emerge from the nonlinear interactions of environmental fluctuations in habitat quality, local density-dependence in reproduction, and dispersal. In the mean-field limit, the correspondence to the Ising model is exact: the fixed points of our dynamical system are given by the equation of state for Weiss mean-field theory under an appropriate mapping of parameters. We have strong evidence that a quantitative correspondence persists, both near and far from the critical point, in the presence of fluctuations. Our results provide a formal connection between equilibrium statistical physics and population biology. This work is supported by the National Science Foundation under Grant No. 1344187.

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.

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.

Compressed quantum simulation of the Ising model.

PubMed

Kraus, B

2011-12-16

Jozsa et al. [Proc. R. Soc. A 466, 809 2009)] have shown that a match gate circuit running on n qubits can be compressed to a universal quantum computation on log(n)+3 qubits. Here, we show how this compression can be employed to simulate the Ising interaction of a 1D chain consisting of n qubits using a universal quantum computer running on log(n) qubits. We demonstrate how the adiabatic evolution can be realized on this exponentially smaller system and how the magnetization, which displays a quantum phase transition, can be measured. This shows that the quantum phase transition of very large systems can be observed experimentally with current technology. © 2011 American Physical Society

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.

Rational group decision making: A random field Ising model at T = 0

NASA Astrophysics Data System (ADS)

Galam, Serge

1997-02-01

A modified version of a finite random field Ising ferromagnetic model in an external magnetic field at zero temperature is presented to describe group decision making. Fields may have a non-zero average. A postulate of minimum inter-individual conflicts is assumed. Interactions then produce a group polarization along one very choice which is however randomly selected. A small external social pressure is shown to have a drastic effect on the polarization. Individual bias related to personal backgrounds, cultural values and past experiences are introduced via quenched local competing fields. They are shown to be instrumental in generating a larger spectrum of collective new choices beyond initial ones. In particular, compromise is found to results from the existence of individual competing bias. Conflict is shown to weaken group polarization. The model yields new psychosociological insights about consensus and compromise in groups.

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

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.

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.

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.

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.

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.

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.

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.

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.

Cancer growth and metastasis as a metaphor of Go gaming: An Ising model approach

PubMed Central

Barradas-Bautista, Didier; Agostino, Mark; Cocho, Germinal

2018-01-01

This work aims for modeling and simulating the metastasis of cancer, via the analogy between the cancer process and the board game Go. In the game of Go, black stones that play first could correspond to a metaphor of the birth, growth, and metastasis of cancer. Moreover, playing white stones on the second turn could correspond the inhibition of cancer invasion. Mathematical modeling and algorithmic simulation of Go may therefore benefit the efforts to deploy therapies to surpass cancer illness by providing insight into the cellular growth and expansion over a tissue area. We use the Ising Hamiltonian, that models the energy exchange in interacting particles, for modeling the cancer dynamics. Parameters in the energy function refer the biochemical elements that induce cancer birth, growth, and metastasis; as well as the biochemical immune system process of defense. PMID:29718932

Cancer growth and metastasis as a metaphor of Go gaming: An Ising model approach.

PubMed

Barradas-Bautista, Didier; Alvarado-Mentado, Matias; Agostino, Mark; Cocho, Germinal

2018-01-01

This work aims for modeling and simulating the metastasis of cancer, via the analogy between the cancer process and the board game Go. In the game of Go, black stones that play first could correspond to a metaphor of the birth, growth, and metastasis of cancer. Moreover, playing white stones on the second turn could correspond the inhibition of cancer invasion. Mathematical modeling and algorithmic simulation of Go may therefore benefit the efforts to deploy therapies to surpass cancer illness by providing insight into the cellular growth and expansion over a tissue area. We use the Ising Hamiltonian, that models the energy exchange in interacting particles, for modeling the cancer dynamics. Parameters in the energy function refer the biochemical elements that induce cancer birth, growth, and metastasis; as well as the biochemical immune system process of defense.

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.

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.

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.

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.

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 .

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.

Localization and Symmetry Breaking in the Quantum Quasiperiodic Ising Glass

NASA Astrophysics Data System (ADS)

Chandran, A.; Laumann, C. R.

2017-07-01

Quasiperiodic modulation can prevent isolated quantum systems from equilibrating by localizing their degrees of freedom. In this article, we show that such systems can exhibit dynamically stable long-range orders forbidden in equilibrium. Specifically, we show that the interplay of symmetry breaking and localization in the quasiperiodic quantum Ising chain produces a quasiperiodic Ising glass stable at all energy densities. The glass order parameter vanishes with an essential singularity at the melting transition with no signatures in the equilibrium properties. The zero-temperature phase diagram is also surprisingly rich, consisting of paramagnetic, ferromagnetic, and quasiperiodically alternating ground-state phases with extended, localized, and critically delocalized low-energy excitations. The system exhibits an unusual quantum Ising transition whose properties are intermediate between those of the clean and infinite randomness Ising transitions. Many of these results follow from a geometric generalization of the Aubry-André duality that we develop. The quasiperiodic Ising glass may be realized in near-term quantum optical experiments.

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

An electromechanical Ising Hamiltonian

PubMed Central

Mahboob, Imran; Okamoto, Hajime; Yamaguchi, Hiroshi

2016-01-01

Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating two-mode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling. PMID:28861469

An electromechanical Ising Hamiltonian.

PubMed

Mahboob, Imran; Okamoto, Hajime; Yamaguchi, Hiroshi

2016-06-01

Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating two-mode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling.

ICE/ISEE plasma wave data analysis

NASA Technical Reports Server (NTRS)

Greenstadt, E. W.

1992-01-01

The interval reported on, from Jan. 1990 to Dec. 1991, has been one of continued processing and archiving of ICE plasma wave (pw) data and transition from analysis of ISEE 3 and ICE cometary data to ICE data taken along its cruise trajectory, where coronal mass ejections are the focus of attention. We have continued to examine with great interest the last year of ISEE 3's precomet phase, when it spent considerable time far downwind from Earth, recording conditions upstream, downstream, and across the very weak, distant flank bow shock. Among other motivations was the apparent similarity of some shock and post shock structures to the signatures of the bow wave surrounding comet Giacobini-Zinner, whose ICE-phase data was revisited. While pursuing detailed, second-order scientific inquiries still pending from the late ISEE 3 recordings, we have also sought to position ourselves for study of CME's by instituting a data processing format new to the ISEE 3/ICE pw detector. Processed detector output has always been summarized and archived in 24-hour segments, with all pw channels individually plotted and stacked one above the next down in frequency, with each channel calibrated separately to keep all data patterns equally visible in the plots, regardless of gross differences in energy content at the various frequencies. Since CME's, with their preceding and following solar wind plasmas, can take more than one day to pass by the spacecraft, a more condensed synoptic view of the pw data is required to identify, let alone assess, CME characteristics than has been afforded by the traditional routines. This requirement is addressed in a major new processing initiative in the past two years. Besides our own ongoing and fresh investigations, we have cooperated, within our resources, with studies conducted extramurally by distant colleagues irrespective of the phase of the ISEE 3/ICE mission under scrutiny. The remainder of this report summarizes our processing activities, our

Transverse fields to tune an Ising-nematic quantum phase transition

NASA Astrophysics Data System (ADS)

Maharaj, Akash V.; Rosenberg, Elliott W.; Hristov, Alexander T.; Berg, Erez; Fernandes, Rafael M.; Fisher, Ian R.; Kivelson, Steven A.

2017-12-01

The paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a quantum phase transition also depends on the dynamics. In the transverse field Ising model, the order parameter is not conserved, and increasing the transverse field enhances quantum fluctuations until they become strong enough to restore the symmetry of the ground state. Ising pseudospins can represent the order parameter of any system with a twofold degenerate broken-symmetry phase, including electronic nematic order associated with spontaneous point-group symmetry breaking. Here, we show for the representative example of orbital-nematic ordering of a non-Kramers doublet that an orthogonal strain or a perpendicular magnetic field plays the role of the transverse field, thereby providing a practical route for tuning appropriate materials to a quantum critical point. While the transverse fields are conjugate to seemingly unrelated order parameters, their nontrivial commutation relations with the nematic order parameter, which can be represented by a Berry-phase term in an effective field theory, intrinsically intertwine the different order parameters.

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

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

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.

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.

Network of time-multiplexed optical parametric oscillators as a coherent Ising machine

NASA Astrophysics Data System (ADS)

Marandi, Alireza; Wang, Zhe; Takata, Kenta; Byer, Robert L.; Yamamoto, Yoshihisa

2014-12-01

Finding the ground states of the Ising Hamiltonian maps to various combinatorial optimization problems in biology, medicine, wireless communications, artificial intelligence and social network. So far, no efficient classical and quantum algorithm is known for these problems and intensive research is focused on creating physical systems—Ising machines—capable of finding the absolute or approximate ground states of the Ising Hamiltonian. Here, we report an Ising machine using a network of degenerate optical parametric oscillators (OPOs). Spins are represented with above-threshold binary phases of the OPOs and the Ising couplings are realized by mutual injections. The network is implemented in a single OPO ring cavity with multiple trains of femtosecond pulses and configurable mutual couplings, and operates at room temperature. We programmed a small non-deterministic polynomial time-hard problem on a 4-OPO Ising machine and in 1,000 runs no computational error was detected.

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.

The bulk, surface and corner free energies of the square lattice Ising model

NASA Astrophysics Data System (ADS)

Baxter, R. J.

2017-01-01

We use Kaufman’s spinor method to calculate the bulk, surface and corner free energies {f}{{b}},{f}{{s}},{f}{{s}}\\prime ,{f}{{c}} of the anisotropic square lattice zero-field Ising model for the ordered ferromagnetic case. For {f}{{b}},{f}{{s}},{f}{{s}}\\prime our results of course agree with the early work of Onsager, McCoy and Wu. We also find agreement with the conjectures made by Vernier and Jacobsen (VJ) for the isotropic case. We note that the corner free energy f c depends only on the elliptic modulus k that enters the working, and not on the argument v, which means that VJ’s conjecture applies for the full anisotropic model. The only aspect of this paper that is new is the actual derivation of f c, but by reporting all four free energies together we can see interesting structures linking them.

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.

2D Spin Crossover Nanoparticles described by the Ising-like model solved in Local Mean-Field Approximation

NASA Astrophysics Data System (ADS)

Eddine Allal, Salah; Linares, Jorge; Boukheddaden, K.; Dahoo, Pierre Richard; de Zela, F.

2017-12-01

Some six-coordinate iron (II) coordination compounds exhibit thermal-, optical-, electrical-, magnetic- and pressure-induced switching between the diamagnetic low-spin (LS, S=0) and the paramagnetic high-spin (HS; S=2) states [1]. This may lead to potential application of these complexes in molecular devices such as temperature and pressure sensors [2]. An Ising-like model has been proposed to explain the occurrence of the thermal hysteresis behaviour [3,4] of this switchable solids. In this contribution, the local mean field approximation is applied to solve the Hamiltonian modelling interactions pertaining to 2D nanoparticles embedded in a magnetically-inactive matrix.

A model of the near-earth plasma environment and application to the ISEE-A and -B orbit

NASA Technical Reports Server (NTRS)

Chan, K. W.; Sawyer, K. W.; Vette, J. I.

1977-01-01

A model of the near-earth environment to obtain a best estimate of the average flux of protons and electrons in the energy range from 0.1 to 100 keV for the International Sun-Earth Explorer (ISEE)-A and -B spacecraft. The possible radiation damage to the thermal coating on these spinning spacecraft is also studied. Applications of the model to other high-altitude satellites can be obtained with the appropriate orbit averaging. This study is the first attempt to synthesize an overall quantitative environment of low-energy particles for high altitude spacecraft, using data from in situ measurements.

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 .

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

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.

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

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.

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.

Censored Glauber Dynamics for the Mean Field Ising Model

NASA Astrophysics Data System (ADS)

Ding, Jian; Lubetzky, Eyal; Peres, Yuval

2009-11-01

We study Glauber dynamics for the Ising model on the complete graph on n vertices, known as the Curie-Weiss Model. It is well known that at high temperature ( β<1) the mixing time is Θ( nlog n), whereas at low temperature ( β>1) it is exp ( Θ( n)). Recently, Levin, Luczak and Peres considered a censored version of this dynamics, which is restricted to non-negative magnetization. They proved that for fixed β>1, the mixing-time of this model is Θ( nlog n), analogous to the high-temperature regime of the original dynamics. Furthermore, they showed cutoff for the original dynamics for fixed β<1. The question whether the censored dynamics also exhibits cutoff remained unsettled. In a companion paper, we extended the results of Levin et al. into a complete characterization of the mixing-time for the Curie-Weiss model. Namely, we found a scaling window of order 1/sqrt{n} around the critical temperature β c =1, beyond which there is cutoff at high temperature. However, determining the behavior of the censored dynamics outside this critical window seemed significantly more challenging. In this work we answer the above question in the affirmative, and establish the cutoff point and its window for the censored dynamics beyond the critical window, thus completing its analogy to the original dynamics at high temperature. Namely, if β=1+ δ for some δ>0 with δ 2 n→∞, then the mixing-time has order ( n/ δ)log ( δ 2 n). The cutoff constant is (1/2+[2(ζ2 β/ δ-1)]-1), where ζ is the unique positive root of g( x)=tanh ( β x)- x, and the cutoff window has order n/ δ.

Degenerate Ising model for atomistic simulation of crystal-melt interfaces

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

Schebarchov, D., E-mail: Dmitri.Schebarchov@gmail.com; Schulze, T. P., E-mail: schulze@math.utk.edu; Hendy, S. C.

2014-02-21

One of the simplest microscopic models for a thermally driven first-order phase transition is an Ising-type lattice system with nearest-neighbour interactions, an external field, and a degeneracy parameter. The underlying lattice and the interaction coupling constant control the anisotropic energy of the phase boundary, the field strength represents the bulk latent heat, and the degeneracy quantifies the difference in communal entropy between the two phases. We simulate the (stochastic) evolution of this minimal model by applying rejection-free canonical and microcanonical Monte Carlo algorithms, and we obtain caloric curves and heat capacity plots for square (2D) and face-centred cubic (3D) latticesmore » with periodic boundary conditions. Since the model admits precise adjustment of bulk latent heat and communal entropy, neither of which affect the interface properties, we are able to tune the crystal nucleation barriers at a fixed degree of undercooling and verify a dimension-dependent scaling expected from classical nucleation theory. We also analyse the equilibrium crystal-melt coexistence in the microcanonical ensemble, where we detect negative heat capacities and find that this phenomenon is more pronounced when the interface is the dominant contributor to the total entropy. The negative branch of the heat capacity appears smooth only when the equilibrium interface-area-to-volume ratio is not constant but varies smoothly with the excitation energy. Finally, we simulate microcanonical crystal nucleation and subsequent relaxation to an equilibrium Wulff shape, demonstrating the model's utility in tracking crystal-melt interfaces at the atomistic level.« 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.

Venous tree separation in the liver: graph partitioning using a non-ising model.

PubMed

O'Donnell, Thomas; Kaftan, Jens N; Schuh, Andreas; Tietjen, Christian; Soza, Grzegorz; Aach, Til

2011-01-01

Entangled tree-like vascular systems are commonly found in the body (e.g., in the peripheries and lungs). Separation of these systems in medical images may be formulated as a graph partitioning problem given an imperfect segmentation and specification of the tree roots. In this work, we show that the ubiquitous Ising-model approaches (e.g., Graph Cuts, Random Walker) are not appropriate for tackling this problem and propose a novel method based on recursive minimal paths for doing so. To motivate our method, we focus on the intertwined portal and hepatic venous systems in the liver. Separation of these systems is critical for liver intervention planning, in particular when resection is involved. We apply our method to 34 clinical datasets, each containing well over a hundred vessel branches, demonstrating its effectiveness.

Programmable superpositions of Ising configurations

NASA Astrophysics Data System (ADS)

Sieberer, Lukas M.; Lechner, Wolfgang

2018-05-01

We present a framework to prepare superpositions of bit strings, i.e., many-body spin configurations, with deterministic programmable probabilities. The spin configurations are encoded in the degenerate ground states of the lattice-gauge representation of an all-to-all connected Ising spin glass. The ground-state manifold is invariant under variations of the gauge degrees of freedom, which take the form of four-body parity constraints. Our framework makes use of these degrees of freedom by individually tuning them to dynamically prepare programmable superpositions. The dynamics combines an adiabatic protocol with controlled diabatic transitions. We derive an effective model that allows one to determine the control parameters efficiently even for large system sizes.

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.

CEP populations observed by ISEE 1

NASA Astrophysics Data System (ADS)

Whitaker, Katherine E.; Chen, Jiasheng; Fritz, Theodore A.

2006-12-01

Observations on October 30, 1978 show the ISEE 1 spacecraft passing though the high-altitude dayside northern cusp region from roughly 16:00 to 18:30 UT, during a slow solar wind period (~380 km/s). More than two orders of magnitude enhancements of the cusp energetic particle (CEP) fluxes are observed along with a depressed and turbulent local magnetic field and both ionospheric and solar wind plasma. The clock angle of the local magnetic field is different from that of the IMF, implying that the spacecraft was indeed inside the magnetosphere. The observed variations of the pitch angle distributions provide a unique opportunity to determine the structure of the cusp. The CEP fluxes were measured at about 8.5 hours MLT when the IMF had both an 8-10 nT duskward and southward component. The dawnside location of the cusp under these IMF conditions is unexpected by the existing models. No obvious time-energy dispersion is measured for the CEP fluxes. The time evolution of the phase space density as the spacecraft crossed the cusp boundary layer exhibits a positive gradient pointed to the high-altitude cusp, indicating a probable cusp source of the energetic particles. Through a careful analysis of the data available, we report the first detailed study of the equatorial orbiting ISEE 1 spacecraft passing through the high altitude cusp region.

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.

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.

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.

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.

Contingency plans for the ISEE-3 libration-point mission

NASA Technical Reports Server (NTRS)

Dunham, D. W.

1979-01-01

During the planning stage of the International Sun-Earth Explorer-3 (ISEE-3) mission, a recovery strategy was developed in case the Delta rocket underperformed during the launch phase. If a large underburn had occurred, the ISEE-3 spacecraft would have been allowed to complete one revolution of its highly elliptical earth orbit. The recovery plan called for a maneuver near perigee to increase the energy of the off-nominal orbit; a relatively small second maneuver would then insert the spacecraft into a new transfer trajectory toward the desired halo orbit target, and a third maneuver would place the spacecraft in the halo orbit. Results of the study showed that a large range of underburns could be corrected for a total nominal velocity deviation cost within the ISEE-3 fuel budget.

Ising Critical Behavior of Inhomogeneous Curie-Weiss Models and Annealed Random Graphs

NASA Astrophysics Data System (ADS)

Dommers, Sander; Giardinà, Cristian; Giberti, Claudio; van der Hofstad, Remco; Prioriello, Maria Luisa

2016-11-01

We study the critical behavior for inhomogeneous versions of the Curie-Weiss model, where the coupling constant {J_{ij}(β)} for the edge {ij} on the complete graph is given by {J_{ij}(β)=β w_iw_j/( {sum_{kin[N]}w_k})}. We call the product form of these couplings the rank-1 inhomogeneous Curie-Weiss model. This model also arises [with inverse temperature {β} replaced by {sinh(β)} ] from the annealed Ising model on the generalized random graph. We assume that the vertex weights {(w_i)_{iin[N]}} are regular, in the sense that their empirical distribution converges and the second moment converges as well. We identify the critical temperatures and exponents for these models, as well as a non-classical limit theorem for the total spin at the critical point. These depend sensitively on the number of finite moments of the weight distribution. When the fourth moment of the weight distribution converges, then the critical behavior is the same as on the (homogeneous) Curie-Weiss model, so that the inhomogeneity is weak. When the fourth moment of the weights converges to infinity, and the weights satisfy an asymptotic power law with exponent {τ} with {τin(3,5)}, then the critical exponents depend sensitively on {τ}. In addition, at criticality, the total spin {S_N} satisfies that {S_N/N^{(τ-2)/(τ-1)}} converges in law to some limiting random variable whose distribution we explicitly characterize.

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

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

Integrated multi-ISE arrays with improved sensitivity, accuracy and precision

NASA Astrophysics Data System (ADS)

Wang, Chunling; Yuan, Hongyan; Duan, Zhijuan; Xiao, Dan

2017-03-01

Increasing use of ion-selective electrodes (ISEs) in the biological and environmental fields has generated demand for high-sensitivity ISEs. However, improving the sensitivities of ISEs remains a challenge because of the limit of the Nernstian slope (59.2/n mV). Here, we present a universal ion detection method using an electronic integrated multi-electrode system (EIMES) that bypasses the Nernstian slope limit of 59.2/n mV, thereby enabling substantial enhancement of the sensitivity of ISEs. The results reveal that the response slope is greatly increased from 57.2 to 1711.3 mV, 57.3 to 564.7 mV and 57.7 to 576.2 mV by electronic integrated 30 Cl- electrodes, 10 F- electrodes and 10 glass pH electrodes, respectively. Thus, a tiny change in the ion concentration can be monitored, and correspondingly, the accuracy and precision are substantially improved. The EIMES is suited for all types of potentiometric sensors and may pave the way for monitoring of various ions with high accuracy and precision because of its high sensitivity.

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.

Quantum Quench Dynamics in the Transverse Field Ising Model at Non-zero Temperatures

NASA Astrophysics Data System (ADS)

Abeling, Nils; Kehrein, Stefan

The recently discovered Dynamical Phase Transition denotes non-analytic behavior in the real time evolution of quantum systems in the thermodynamic limit and has been shown to occur in different systems at zero temperature [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)]. In this talk we present the extension of the analysis to non-zero temperature by studying a generalized form of the Loschmidt echo, the work distribution function, of a quantum quench in the transverse field Ising model. Although the quantitative behavior at non-zero temperatures still displays features derived from the zero temperature non-analyticities, it is shown that in this model dynamical phase transitions do not exist if T > 0 . This is a consequence of the system being initialized in a thermal state. Moreover, we elucidate how the Tasaki-Crooks-Jarzynski relation can be exploited as a symmetry relation for a global quench or to obtain the change of the equilibrium free energy density. This work was supported through CRC SFB 1073 (Project B03) of the Deutsche Forschungsgemeinschaft (DFG).

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).

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.

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.

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.

ISEES: an institute for sustainable software to accelerate environmental science

NASA Astrophysics Data System (ADS)

Jones, M. B.; Schildhauer, M.; Fox, P. A.

2013-12-01

Software is essential to the full science lifecycle, spanning data acquisition, processing, quality assessment, data integration, analysis, modeling, and visualization. Software runs our meteorological sensor systems, our data loggers, and our ocean gliders. Every aspect of science is impacted by, and improved by, software. Scientific advances ranging from modeling climate change to the sequencing of the human genome have been rendered possible in the last few decades due to the massive improvements in the capabilities of computers to process data through software. This pivotal role of software in science is broadly acknowledged, while simultaneously being systematically undervalued through minimal investments in maintenance and innovation. As a community, we need to embrace the creation, use, and maintenance of software within science, and address problems such as code complexity, openness,reproducibility, and accessibility. We also need to fully develop new skills and practices in software engineering as a core competency in our earth science disciplines, starting with undergraduate and graduate education and extending into university and agency professional positions. The Institute for Sustainable Earth and Environmental Software (ISEES) is being envisioned as a community-driven activity that can facilitate and galvanize activites around scientific software in an analogous way to synthesis centers such as NCEAS and NESCent that have stimulated massive advances in ecology and evolution. We will describe the results of six workshops (Science Drivers, Software Lifecycles, Software Components, Workforce Development and Training, Sustainability and Governance, and Community Engagement) that have been held in 2013 to envision such an institute. We will present community recommendations from these workshops and our strategic vision for how ISEES will address the technical issues in the software lifecycle, sustainability of the whole software ecosystem, and the critical

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.

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.

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

Solar wind-magnetosphere coupling and the distant magnetotail: ISEE-3 observations

NASA Technical Reports Server (NTRS)

Slavin, J. A.; Smith, E. J.; Sibeck, D. G.; Baker, D. N.; Zwickl, R. D.; Akasofu, S. I.; Lepping, R. P.

1985-01-01

ISEE-3 Geotail observations are used to investigate the relationship between the interplanetary magnetic field, substorm activity, and the distant magnetotail. Magnetic field and plasma observations are used to present evidence for the existence of a quasi-permanent, curved reconnection neutral line in the distant tail. The distance to the neutral line varies from absolute value of X = 120 to 140 R/sub e near the center of the tail to beyond absolute value of X = 200 R/sub e at the flanks. Downstream of the neutral line the plasma sheet magnetic field is shown to be negative and directly proportional to negative B/sub z in the solar wind as observed by IMP-8. V/sub x in the distant plasma sheet is also found to be proportional to IMF B/sub z with southward IMF producing the highest anti-solar flow velocities. A global dayside reconnection efficiency of 20 +- 5% is derived from the ISEE-3/IMP-8 magnetic field comparisons. Substorm activity, as measured by the AL index, produces enhanced negative B/sub z and tailward V/sub x in the distant plasma sheet in agreement with the basic predictions of the reconnection-based models of substorms. The rate of magnetic flux transfer out of the tail as a function of AL is found to be consistent with previous near-Earth studies. Similarly, the mass and energy fluxes carried by plasma sheet flow down the tail are consistent with theoretical mass and energy budgets for an open magnetosphere. In summary, the ISEE-3 Geotail observations appear to provide good support for reconnection models of solar wind-magnetosphere coupling and substorm energy rates.

The 2014 Earth return of the ISEE-3/ICE spacecraft

NASA Astrophysics Data System (ADS)

Dunham, David W.; Farquhar, Robert W.; Loucks, Michel; Roberts, Craig E.; Wingo, Dennis; Cowing, Keith L.; Garcia, Leonard N.; Craychee, Tim; Nickel, Craig; Ford, Anthony; Colleluori, Marco; Folta, David C.; Giorgini, Jon D.; Nace, Edward; Spohr, John E.; Dove, William; Mogk, Nathan; Furfaro, Roberto; Martin, Warren L.

2015-05-01

In 1978, the 3rd International Sun-Earth Explorer (ISEE-3) became the first libration-point mission, about the Sun-Earth L1 point. Four years later, a complex series of lunar swingbys and small propulsive maneuvers ejected ISEE-3 from the Earth-Moon system, to fly by a comet (Giacobini-Zinner) for the first time in 1985, as the rechristened International Cometary Explorer (ICE). In its heliocentric orbit, ISEE-3/ICE slowly drifted around the Sun to return to the Earth's vicinity in 2014. Maneuvers in 1986 targeted a 2014 August 10th lunar swingby to recapture ISEE-3 into Earth orbit. In 1999, ISEE-3/ICE passed behind the Sun; after that, tracking of the spacecraft ceased and its control center at Goddard was shut down. In 2013, meetings were held to assess the viability of "re-awakening" ISEE-3. The goal was to target the 2014 lunar swingby, to recapture the spacecraft back into a halo-like Sun-Earth L1 orbit. However, special hardware for communicating with the spacecraft via NASA's Deep Space Network stations was discarded after 1999, and NASA had no funds to reconstruct the lost equipment. After ISEE-3's carrier signal was detected on March 1st with the 20 m antenna at Bochum, Germany, Skycorp, Inc. decided to initiate the ISEE-3 Reboot Project, to use software-defined radio with a less costly S-band transmitter that was purchased with a successful RocketHub crowdsourcing effort. NASA granted Skycorp permission to command the spacecraft. Commanding was successfully accomplished using the 300 m radio telescope at Arecibo. New capture trajectories were computed, including trajectories that would target the August lunar swingby and use a second ΔV (velocity change) that could target later lunar swingbys that would allow capture into almost any desired final orbit, including orbits about either the Sun-Earth L1 or L2 points, a lunar distant retrograde orbit, or targeting a flyby of the Earth-approaching active Comet Wirtanen in 2018. A tiny spinup maneuver was

The square lattice Ising model on the rectangle II: finite-size scaling limit

NASA Astrophysics Data System (ADS)

Hucht, Alfred

2017-06-01

Based on the results published recently (Hucht 2017 J. Phys. A: Math. Theor. 50 065201), the universal finite-size contributions to the free energy of the square lattice Ising model on the L× M rectangle, with open boundary conditions in both directions, are calculated exactly in the finite-size scaling limit L, M\\to∞ , T\\to Tc , with fixed temperature scaling variable x\\propto(T/Tc-1)M and fixed aspect ratio ρ\\propto L/M . We derive exponentially fast converging series for the related Casimir potential and Casimir force scaling functions. At the critical point T=Tc we confirm predictions from conformal field theory (Cardy and Peschel 1988 Nucl. Phys. B 300 377, Kleban and Vassileva 1991 J. Phys. A: Math. Gen. 24 3407). The presence of corners and the related corner free energy has dramatic impact on the Casimir scaling functions and leads to a logarithmic divergence of the Casimir potential scaling function at criticality.

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.

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.

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.

Identification of ground-state spin ordering in antiferromagnetic transition metal oxides using the Ising model and a genetic algorithm

PubMed Central

Lee, Kyuhyun; Youn, Yong; Han, Seungwu

2017-01-01

Abstract We identify ground-state collinear spin ordering in various antiferromagnetic transition metal oxides by constructing the Ising model from first-principles results and applying a genetic algorithm to find its minimum energy state. The present method can correctly reproduce the ground state of well-known antiferromagnetic oxides such as NiO, Fe2O3, Cr2O3 and MnO2. Furthermore, we identify the ground-state spin ordering in more complicated materials such as Mn3O4 and CoCr2O4. PMID:28458746

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.

Highlighting the Structure-Function Relationship of the Brain with the Ising Model and Graph Theory

PubMed Central

Das, T. K.; Abeyasinghe, P. M.; Crone, J. S.; Sosnowski, A.; Laureys, S.; Owen, A. M.; Soddu, A.

2014-01-01

With the advent of neuroimaging techniques, it becomes feasible to explore the structure-function relationships in the brain. When the brain is not involved in any cognitive task or stimulated by any external output, it preserves important activities which follow well-defined spatial distribution patterns. Understanding the self-organization of the brain from its anatomical structure, it has been recently suggested to model the observed functional pattern from the structure of white matter fiber bundles. Different models which study synchronization (e.g., the Kuramoto model) or global dynamics (e.g., the Ising model) have shown success in capturing fundamental properties of the brain. In particular, these models can explain the competition between modularity and specialization and the need for integration in the brain. Graphing the functional and structural brain organization supports the model and can also highlight the strategy used to process and organize large amount of information traveling between the different modules. How the flow of information can be prevented or partially destroyed in pathological states, like in severe brain injured patients with disorders of consciousness or by pharmacological induction like in anaesthesia, will also help us to better understand how global or integrated behavior can emerge from local and modular interactions. PMID:25276772

Large-Scale Simulation of Multi-Asset Ising Financial Markets

NASA Astrophysics Data System (ADS)

Takaishi, Tetsuya

2017-03-01

We perform a large-scale simulation of an Ising-based financial market model that includes 300 asset time series. The financial system simulated by the model shows a fat-tailed return distribution and volatility clustering and exhibits unstable periods indicated by the volatility index measured as the average of absolute-returns. Moreover, we determine that the cumulative risk fraction, which measures the system risk, changes at high volatility periods. We also calculate the inverse participation ratio (IPR) and its higher-power version, IPR6, from the absolute-return cross-correlation matrix. Finally, we show that the IPR and IPR6 also change at high volatility periods.

Applications of ISES for vegetation and land use

NASA Technical Reports Server (NTRS)

Wilson, R. Gale

1990-01-01

Remote sensing relative to applications involving vegetation cover and land use is reviewed to consider the potential benefits to the Earth Observing System (Eos) of a proposed Information Sciences Experiment System (ISES). The ISES concept has been proposed as an onboard experiment and computational resource to support advanced experiments and demonstrations in the information and earth sciences. Embedded in the concept is potential for relieving the data glut problem, enhancing capabilities to meet real-time needs of data users and in-situ researchers, and introducing emerging technology to Eos as the technology matures. These potential benefits are examined in the context of state-of-the-art research activities in image/data processing and management.

Frustration and correlations in stacked triangular-lattice Ising antiferromagnets

NASA Astrophysics Data System (ADS)

Burnell, F. J.; Chalker, J. T.

2015-12-01

We study multilayer triangular-lattice Ising antiferromagnets with interlayer interactions that are weak and frustrated in an abc stacking. By analyzing a coupled height model description of these systems, we show that they exhibit a classical spin liquid regime at low temperature, in which both intralayer and interlayer correlations are strong but there is no long-range order. Diffuse scattering in this regime is concentrated on a helix in reciprocal space, as observed for charge ordering in the materials LuFe2O4 and YbFe2O4 .

Hysteresis in DNA compaction by Dps is described by an Ising model

PubMed Central

Vtyurina, Natalia N.; Dulin, David; Docter, Margreet W.; Meyer, Anne S.; Dekker, Nynke H.; Abbondanzieri, Elio A.

2016-01-01

In all organisms, DNA molecules are tightly compacted into a dynamic 3D nucleoprotein complex. In bacteria, this compaction is governed by the family of nucleoid-associated proteins (NAPs). Under conditions of stress and starvation, an NAP called Dps (DNA-binding protein from starved cells) becomes highly up-regulated and can massively reorganize the bacterial chromosome. Although static structures of Dps–DNA complexes have been documented, little is known about the dynamics of their assembly. Here, we use fluorescence microscopy and magnetic-tweezers measurements to resolve the process of DNA compaction by Dps. Real-time in vitro studies demonstrated a highly cooperative process of Dps binding characterized by an abrupt collapse of the DNA extension, even under applied tension. Surprisingly, we also discovered a reproducible hysteresis in the process of compaction and decompaction of the Dps–DNA complex. This hysteresis is extremely stable over hour-long timescales despite the rapid binding and dissociation rates of Dps. A modified Ising model is successfully applied to fit these kinetic features. We find that long-lived hysteresis arises naturally as a consequence of protein cooperativity in large complexes and provides a useful mechanism for cells to adopt unique epigenetic states. PMID:27091987

A Meloidogyne incognita effector MiISE5 suppresses programmed cell death to promote parasitism in host plant.

PubMed

Shi, Qianqian; Mao, Zhenchuan; Zhang, Xi; Zhang, Xiaoping; Wang, Yunsheng; Ling, Jian; Lin, Runmao; Li, Denghui; Kang, Xincong; Sun, Wenxian; Xie, Bingyan

2018-05-08

Root-knot nematodes (RKNs) are highly specialized parasites that interact with their host plants using a range of strategies. The esophageal glands are the main places where nematodes synthesize effector proteins, which play central roles in successful invasion. The Meloidogyne incognita effector MiISE5 is exclusively expressed within the subventral esophageal cells and is upregulated during early parasitic stages. In this study, we show that MiISE5 can be secreted to barley cells through infectious hyphae of Magnaporthe oryzae. Transgenic Arabidopsis plants expressing MiISE5 became significantly more susceptible to M. incognita. Inversely, the tobacco rattle virus (TRV)-mediated silence of MiISE5 decreased nematode parasitism. Moreover, transient expression of MiISE5 suppressed cell death caused by Burkholderia glumae in Nicotiana benthamiana. Based on transcriptome analysis of MiISE5 transgenic sample and the wild-type (WT) sample, we obtained 261 DEGs, and the results of GO and KEGG enrichment analysis indicate that MiISE5 can interfere with various metabolic and signaling pathways, especially the JA signaling pathway, to facilitate nematode parasitism. Results from the present study suggest that MiISE5 plays an important role during the early stages of parasitism and provides evidence to decipher the molecular mechanisms underlying the manipulation of host immune defense responses by M. incognita.

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.

ISEE/ICE plasma wave data analysis

NASA Technical Reports Server (NTRS)

Greenstadt, E. W.

1989-01-01

The work performed for the period 1 Jan. 1985 to 30 Oct. 1989 is presented. The objective was to provide reduction and analysis of data from a scientific instrument designed to study solar wind and plasma wave phenomena on the International Sun Earth Explorer 3 (ISEE-3)/International Cometary Explorer (ICE) missions.

Random-field Ising model on isometric lattices: Ground states and non-Porod scattering

NASA Astrophysics Data System (ADS)

Bupathy, Arunkumar; Banerjee, Varsha; Puri, Sanjay

2016-01-01

We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δc at zero temperature with high accuracy. For the SC lattice, our estimate (Δc=2.278 ±0.002 ) is consistent with earlier reports. For the BCC and FCC lattices, Δc=3.316 ±0.002 and 5.160 ±0.002 , respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α =0.5 ±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy Ei(L ) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.

The In Situ Enzymatic Screening (ISES) Approach to Reaction Discovery and Catalyst Identification.

PubMed

Swyka, Robert A; Berkowitz, David B

2017-12-14

The importance of discovering new chemical transformations and/or optimizing catalytic combinations has led to a flurry of activity in reaction screening. The in situ enzymatic screening (ISES) approach described here utilizes biological tools (enzymes/cofactors) to advance chemistry. The protocol interfaces an organic reaction layer with an adjacent aqueous layer containing reporting enzymes that act upon the organic reaction product, giving rise to a spectroscopic signal. ISES allows the experimentalist to rapidly glean information on the relative rates of a set of parallel organic/organometallic reactions under investigation, without the need to quench the reactions or draw aliquots. In certain cases, the real-time enzymatic readout also provides information on sense and magnitude of enantioselectivity and substrate specificity. This article contains protocols for single-well (relative rate) and double-well (relative rate/enantiomeric excess) ISES, in addition to a colorimetric ISES protocol and a miniaturized double-well procedure. © 2017 by John Wiley & Sons, Inc. Copyright © 2017 John Wiley & Sons, Inc.

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.

Phase diagram of the frustrated J 1 ‑ J 2 transverse field Ising model on the square lattice

NASA Astrophysics Data System (ADS)

Sadrzadeh, M.; Langari, A.

2018-03-01

We study the zero-temperature phase diagram of transverse field Ising model on the J 1 ‑ J 2 square lattice. In zero magnetic field, the model has a classical Néel phase for J 2/J 1 < 0.5 and an antiferromagnetic collinear phase for J 2/J 1 > 0.5. We incorporate harmonic fluctuations by using linear spin wave theory (LSWT) with single spin flip excitations above a magnetic order background and obtain the phase diagram of the model in this approximation. We find that harmonic quantum fluctuations of LSWT fail to lift the large degeneracy at J 2/J 1 = 0.5 and exhibit some inconsistent regions on the phase diagram. However, we show that anharmonic fluctuations of cluster operator approach (COA) resolve the inconsistency of the LSWT, which reveals a string-valence bond solid ordered phase for the highly frustrated region.

ICE/ISEE plasma wave data analysis

NASA Technical Reports Server (NTRS)

Greenstadt, E. W.; Moses, S. L.

1993-01-01

This report is one of the final processing of ICE plasma wave (pw) data and analysis of late ISEE 3, ICE cometary, and ICE cruise trajectory data, where coronal mass ejections (CME's) were the first locus of attention. Interest in CME's inspired an effort to represent our pw data in a condensed spectrogram format that facilitated rapid digestion of interplanetary phenomena on long (greater than 1 day) time scales. The format serendipitously allowed us to also examine earth-orbiting data from a new perspective, invigorating older areas of investigation in Earth's immediate environment. We, therefore, continued to examine with great interest the last year of ISEE 3's precomet phase, when it spent considerable time far downwind from Earth, recording for days on end conditions upstream, downstream, and across the very weak, distant flank bow shock. Among other motivations has been the apparent similarity of some shock and post shock structures to the signatures of the bow wave surrounding comet Giacobini-Zinner, whose ICE-phase data we revisited.

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.

Ising lattices with +/-J second-nearest-neighbor interactions

NASA Astrophysics Data System (ADS)

Ramírez-Pastor, A. J.; Nieto, F.; Vogel, E. E.

1997-06-01

Second-nearest-neighbor interactions are added to the usual nearest-neighbor Ising Hamiltonian for square lattices in different ways. The starting point is a square lattice where half the nearest-neighbor interactions are ferromagnetic and the other half of the bonds are antiferromagnetic. Then, second-nearest-neighbor interactions can also be assigned randomly or in a variety of causal manners determined by the nearest-neighbor interactions. In the present paper we consider three causal and three random ways of assigning second-nearest-neighbor exchange interactions. Several ground-state properties are then calculated for each of these lattices:energy per bond ɛg, site correlation parameter pg, maximal magnetization μg, and fraction of unfrustrated bonds hg. A set of 500 samples is considered for each size N (number of spins) and array (way of distributing the N spins). The properties of the original lattices with only nearest-neighbor interactions are already known, which allows realizing the effect of the additional interactions. We also include cubic lattices to discuss the distinction between coordination number and dimensionality. Comparison with results for triangular and honeycomb lattices is done at specific points.

Plasma wave experiment for the ISEE-3 mission

NASA Technical Reports Server (NTRS)

Scarf, F. L.

1982-01-01

Analysis of data from a scientific instrument designed to study solar wind and plasma wave phenomena on the ISEE-3 mission is presented. The performance of work on the data analysis phase is summarized.

Effective field renormalization group approach for Ising lattice spin systems

NASA Astrophysics Data System (ADS)

Fittipaldi, Ivon P.

1994-03-01

A new applicable real-space renormalization group framework (EFRG) for computing the critical properties of Ising lattice spin systems is presented. The method, which follows up the same strategy of the mean-field renormalization group scheme (MFRG), is based on rigorous Ising spin identities and utilizes a convenient differential operator expansion technique. Within this scheme, in contrast with the usual mean-field type of equation of state, all the relevant self-spin correlations are taken exactly into account. The results for the critical coupling and the critical exponent v, for the correlation length, are very satisfactory and it is shown that this technique leads to rather accurate results which represent a remarkable improvement on those obtained from the standard MFRG method. In particular, it is shown that the present EFRG approach correctly distinguishes the geometry of the lattice structure even when employing its simplest size-cluster version. Owing to its simplicity we also comment on the wide applicability of the present method to problems in crystalline and disordered Ising spin systems.

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.

Sparse High Dimensional Models in Economics

PubMed Central

Fan, Jianqing; Lv, Jinchi; Qi, Lei

2010-01-01

This paper reviews the literature on sparse high dimensional models and discusses some applications in economics and finance. Recent developments of theory, methods, and implementations in penalized least squares and penalized likelihood methods are highlighted. These variable selection methods are proved to be effective in high dimensional sparse modeling. The limits of dimensionality that regularization methods can handle, the role of penalty functions, and their statistical properties are detailed. Some recent advances in ultra-high dimensional sparse modeling are also briefly discussed. PMID:22022635

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.

Ising Processing Units: Potential and Challenges for Discrete Optimization

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

Coffrin, Carleton James; Nagarajan, Harsha; Bent, Russell Whitford

The recent emergence of novel computational devices, such as adiabatic quantum computers, CMOS annealers, and optical parametric oscillators, presents new opportunities for hybrid-optimization algorithms that leverage these kinds of specialized hardware. In this work, we propose the idea of an Ising processing unit as a computational abstraction for these emerging tools. Challenges involved in using and bench- marking these devices are presented, and open-source software tools are proposed to address some of these challenges. The proposed benchmarking tools and methodology are demonstrated by conducting a baseline study of established solution methods to a D-Wave 2X adiabatic quantum computer, one examplemore » of a commercially available Ising processing unit.« less

Ground-state candidate for the classical dipolar kagome Ising antiferromagnet

NASA Astrophysics Data System (ADS)

Chioar, I. A.; Rougemaille, N.; Canals, B.

2016-06-01

We have investigated the low-temperature thermodynamic properties of the classical dipolar kagome Ising antiferromagnet using Monte Carlo simulations, in the quest for the ground-state manifold. In spite of the limitations of a single-spin-flip approach, we managed to identify certain ordering patterns in the low-temperature regime and we propose a candidate for this unknown state. This configuration presents some intriguing features and is fully compatible with the extrapolations of the at-equilibrium thermodynamic behavior sampled so far, making it a very likely choice for the dipolar long-range ordered state of the classical kagome Ising antiferromagnet.

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.

Extra-dimensional models on the lattice

DOE PAGES

Knechtli, Francesco; Rinaldi, Enrico

2016-08-05

In this paper we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is generated by quantum corrections and is protected from divergences by the higher dimensional gauge symmetry. Dimensional reduction to four dimensions can occur through compactification or localization. Gauge-Higgs unification models are often studied using perturbation theory. Numerical lattice simulations are used to go beyond these perturbative expectations and to include nonperturbative effects. We describe the known perturbative predictions and their fate in the strongly-coupled regime formore » various extra-dimensional models.« less

Comparison of the exact thermodynamics of the AF Blume-Emery-Grifiths and of the spin-1 ferromagnetic Ising models

NASA Astrophysics Data System (ADS)

Corrêa Silva, E. V.; Thomaz, M. T.

2016-11-01

We study in detail the thermodynamics of the anti-ferromagnetic Blume-Emery-Griffiths (AF BEG) model in the presence of a longitudinal magnetic field. Its thermodynamics is derived from the exact Helmholtz free energy (HFE) of the model, valid for T > 0. Numerical simulations of this model on a periodic space chain with 10 sites (N=10) yield the energy spectra of the model at K/J = 2 for D/J = 1 and D/J = 2, thus helping us compare, for a broad range of temperature, how some (per site) thermodynamic functions with the same value of K/J but distinct values of D/J behave, namely: the z-component of the magnetization, the specific heat and the entropy. These thermodynamic functions of the AF BEG model at K/|J| = 2 are compared to those of the spin-1 ferromagnetic Ising model with D/|J| > 1.5, for which the T=0 phase diagrams of both models are identical. This comparison is done in a large interval of temperature.

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.

Rigorous joining of advanced reduced-dimensional beam models to three-dimensional finite element models

NASA Astrophysics Data System (ADS)

Song, Huimin

In the aerospace and automotive industries, many finite element analyses use lower-dimensional finite elements such as beams, plates and shells, to simplify the modeling. These simplified models can greatly reduce the computation time and cost; however, reduced-dimensional models may introduce inaccuracies, particularly near boundaries and near portions of the structure where reduced-dimensional models may not apply. Another factor in creation of such models is that beam-like structures frequently have complex geometry, boundaries and loading conditions, which may make them unsuitable for modeling with single type of element. The goal of this dissertation is to develop a method that can accurately and efficiently capture the response of a structure by rigorous combination of a reduced-dimensional beam finite element model with a model based on full two-dimensional (2D) or three-dimensional (3D) finite elements. The first chapter of the thesis gives the background of the present work and some related previous work. The second chapter is focused on formulating a system of equations that govern the joining of a 2D model with a beam model for planar deformation. The essential aspect of this formulation is to find the transformation matrices to achieve deflection and load continuity on the interface. Three approaches are provided to obtain the transformation matrices. An example based on joining a beam to a 2D finite element model is examined, and the accuracy of the analysis is studied by comparing joint results with the full 2D analysis. The third chapter is focused on formulating the system of equations for joining a beam to a 3D finite element model for static and free-vibration problems. The transition between the 3D elements and beam elements is achieved by use of the stress recovery technique of the variational-asymptotic method as implemented in VABS (the Variational Asymptotic Beam Section analysis). The formulations for an interface transformation matrix and

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.

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

A Standardized Generalized Dimensionality Discrepancy Measure and a Standardized Model-Based Covariance for Dimensionality Assessment for Multidimensional Models

ERIC Educational Resources Information Center

Levy, Roy; Xu, Yuning; Yel, Nedim; Svetina, Dubravka

2015-01-01

The standardized generalized dimensionality discrepancy measure and the standardized model-based covariance are introduced as tools to critique dimensionality assumptions in multidimensional item response models. These tools are grounded in a covariance theory perspective and associated connections between dimensionality and local independence.…

Plasma wave experiment for the ISEE-3 mission

NASA Technical Reports Server (NTRS)

Scarf, F. L.

1983-01-01

An analysis of data from a scientific instrument designed to study solar wind and plasma wave phenomena on the ISEE-3 Mission is provided. Work on the data analysis phase of the contract from 1 October 1982 through 30 March 1983 is summarized.

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.

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.

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.

System for generating two-dimensional masks from a three-dimensional model using topological analysis

DOEpatents

Schiek, Richard [Albuquerque, NM

2006-06-20

A method of generating two-dimensional masks from a three-dimensional model comprises providing a three-dimensional model representing a micro-electro-mechanical structure for manufacture and a description of process mask requirements, reducing the three-dimensional model to a topological description of unique cross sections, and selecting candidate masks from the unique cross sections and the cross section topology. The method further can comprise reconciling the candidate masks based on the process mask requirements description to produce two-dimensional process masks.

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.

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.

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.

Perturbative Normal Form Theory for the 2D Random-Field Ising Model

NASA Astrophysics Data System (ADS)

Hayden, Lorien; Raju, Archishman; Sethna, James

Bifurcation theory is important to explain scaling in many systems. For the equilibrium random-field Ising model (RFIM) in 2D, the exponentially diverging correlation length can be derived directly from the RG flows which form a pitchfork bifurcation: dw/dl = -ɛ/2 w +w3 (Bray and Moore 1985). Our perturbative normal form theory (PNFT) predicts a term w5 to be critical in describing the behavior - it cannot be removed through an analytic change of coordinates. The new form of the correlation length produced has been observed to occur in leading order without explanation (Meinke and Middleton 2005). Performing simulations of the non-equilibrium RFIM on a Voronoi lattice uncovers a transcritical bifurcation of the form dw/dl = -ɛ/2 w +w2 + Bw3 . The RG flows determined by PNFT in this case lead directly to a form for the appropriate invariant scaling combination: s exp (- 1 / σνw) (1/w + B) C + B / σν . Using this scaling combination yields a collapse which was not possible to achieve using standard methods such as Widom scaling arguments. Further, the scaling extends over a decade in the magnitude of the disorder and explains behavior down to avalanche sizes of three, the edge of complexity. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No . DGE-1144153 and a Cornell Fellowship.

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.

Concentration data and dimensionality in groundwater models: evaluation using inverse modelling

USGS Publications Warehouse

Barlebo, H.C.; Hill, M.C.; Rosbjerg, D.; Jensen, K.H.

1998-01-01

A three-dimensional inverse groundwater flow and transport model that fits hydraulic-head and concentration data simultaneously using nonlinear regression is presented and applied to a layered sand and silt groundwater system beneath the Grindsted Landfill in Denmark. The aquifer is composed of rather homogeneous hydrogeologic layers. Two issues common to groundwater flow and transport modelling are investigated: 1) The accuracy of simulated concentrations in the case of calibration with head data alone; and 2) The advantages and disadvantages of using a two-dimensional cross-sectional model instead of a three-dimensional model to simulate contaminant transport when the source is at the land surface. Results show that using only hydraulic heads in the nonlinear regression produces a simulated plume that is profoundly different from what is obtained in a calibration using both hydraulic-head and concentration data. The present study provides a well-documented example of the differences that can occur. Representing the system as a two-dimensional cross-section obviously omits some of the system dynamics. It was, however, possible to obtain a simulated plume cross-section that matched the actual plume cross-section well. The two-dimensional model execution times were about a seventh of those for the three-dimensional model, but some difficulties were encountered in representing the spatially variable source concentrations and less precise simulated concentrations were calculated by the two-dimensional model compared to the three-dimensional model. Summed up, the present study indicates that three dimensional modelling using both hydraulic heads and concentrations in the calibration should be preferred in the considered type of transport studies.

Validation of a Real-Time ISE Methodology to Quantify the Influence of Inhibitors of Demineralization Kinetics in vitro Using a Hydroxyapatite Model System.

PubMed

Huang, Wei-Te; Shahid, Saroash; Anderson, Paul

2018-05-25

The aim was to validate a novel protocol to measure the cariostatic efficacies of demineralization inhibitors by repeating previous SMR (scanning microradiography) studies investigating the dose response of Zn2+ and F- on demineralization kinetics in vitro using real-time Ca2+ ion selective electrodes (ISEs). In this study, Ca2+ release was used as a proxy for the extent of demineralization. Forty-eight hydroxyapatite (HAP) discs were allocated into 16 groups (n = 3) and adding either increasing [Zn2+], or [F-], similar to those used in the previous SMR studies. Each HAP disc was immersed in 50 mL, pH 4.0, buffered acetic acid for 1 h, and real-time ISE methodology was used to monitor the rate of increase in [Ca2+] in the demineralization solution. Next, either zinc acetate or sodium fluoride was added into each demineralization solution accordingly. Then after each [Zn2+] or [F-] addition, the HAP disc was further demineralized for 1 h, and ISE measurements were continued. The percentage reduction in the rate of calcium loss from hydroxyapatite (PRCLHAP) at each [Zn2+] or [F-] was calculated from the decrease in Ca2+ release rate, similar to that used in the previous SMR studies. A log-linear relationship between mean PRCLHAP and inhibitor concentration was found for both Zn2+ and F-, similar to that reported for each ion in the previous SMR studies. In conclusion, real-time Ca2+ ISE systems can be used to measure the cariostatic efficacies of demineralization inhibitors. © 2018 S. Karger AG, Basel.

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.

Effect of platykurtic and leptokurtic distributions in the random-field Ising model: mean-field approach.

PubMed

Duarte Queirós, Sílvio M; Crokidakis, Nuno; Soares-Pinto, Diogo O

2009-07-01

The influence of the tail features of the local magnetic field probability density function (PDF) on the ferromagnetic Ising model is studied in the limit of infinite range interactions. Specifically, we assign a quenched random field whose value is in accordance with a generic distribution that bears platykurtic and leptokurtic distributions depending on a single parameter tau<3 to each site. For tau<5/3, such distributions, which are basically Student-t and r distribution extended for all plausible real degrees of freedom, present a finite standard deviation, if not the distribution has got the same asymptotic power-law behavior as a alpha-stable Lévy distribution with alpha=(3-tau)/(tau-1). For every value of tau, at specific temperature and width of the distribution, the system undergoes a continuous phase transition. Strikingly, we impart the emergence of an inflexion point in the temperature-PDF width phase diagrams for distributions broader than the Cauchy-Lorentz (tau=2) which is accompanied with a divergent free energy per spin (at zero temperature).

Dimensional reduction for a SIR type model

NASA Astrophysics Data System (ADS)

Cahyono, Edi; Soeharyadi, Yudi; Mukhsar

2018-03-01

Epidemic phenomena are often modeled in the form of dynamical systems. Such model has also been used to model spread of rumor, spread of extreme ideology, and dissemination of knowledge. Among the simplest is SIR (susceptible, infected and recovered) model, a model that consists of three compartments, and hence three variables. The variables are functions of time which represent the number of subpopulations, namely suspect, infected and recovery. The sum of the three is assumed to be constant. Hence, the model is actually two dimensional which sits in three-dimensional ambient space. This paper deals with the reduction of a SIR type model into two variables in two-dimensional ambient space to understand the geometry and dynamics better. The dynamics is studied, and the phase portrait is presented. The two dimensional model preserves the equilibrium and the stability. The model has been applied for knowledge dissemination, which has been the interest of knowledge management.

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.

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

One-dimensional GIS-based model compared with a two-dimensional model in urban floods simulation.

PubMed

Lhomme, J; Bouvier, C; Mignot, E; Paquier, A

2006-01-01

A GIS-based one-dimensional flood simulation model is presented and applied to the centre of the city of Nîmes (Gard, France), for mapping flow depths or velocities in the streets network. The geometry of the one-dimensional elements is derived from the Digital Elevation Model (DEM). The flow is routed from one element to the next using the kinematic wave approximation. At the crossroads, the flows in the downstream branches are computed using a conceptual scheme. This scheme was previously designed to fit Y-shaped pipes junctions, and has been modified here to fit X-shaped crossroads. The results were compared with the results of a two-dimensional hydrodynamic model based on the full shallow water equations. The comparison shows that good agreements can be found in the steepest streets of the study zone, but differences may be important in the other streets. Some reasons that can explain the differences between the two models are given and some research possibilities are proposed.

Real-time ISEE data system

NASA Technical Reports Server (NTRS)

Tsurutani, B. T.; Baker, D. N.

1979-01-01

A real-time ISEE data system directed toward predicting geomagnetic substorms and storms is discussed. Such a system may allow up to 60+ minutes advance warning of magnetospheric substorms and up to 30 minute warnings of geomagnetic storms (and other disturbances) induced by high-speed streams and solar flares. The proposed system utilizes existing capabilities of several agencies (NASA, NOAA, USAF), and thereby minimizes costs. This same concept may be applicable to data from other spacecraft, and other NASA centers; thus, each individual experimenter can receive quick-look data in real time at his or her base institution.

Exploring load, velocity, and surface disorder dependence of friction with one-dimensional and two-dimensional models.

PubMed

Dagdeviren, Omur E

2018-08-03

The effect of surface disorder, load, and velocity on friction between a single asperity contact and a model surface is explored with one-dimensional and two-dimensional Prandtl-Tomlinson (PT) models. We show that there are fundamental physical differences between the predictions of one-dimensional and two-dimensional models. The one-dimensional model estimates a monotonic increase in friction and energy dissipation with load, velocity, and surface disorder. However, a two-dimensional PT model, which is expected to approximate a tip-sample system more realistically, reveals a non-monotonic trend, i.e. friction is inert to surface disorder and roughness in wearless friction regime. The two-dimensional model discloses that the surface disorder starts to dominate the friction and energy dissipation when the tip and the sample interact predominantly deep into the repulsive regime. Our numerical calculations address that tracking the minimum energy path and the slip-stick motion are two competing effects that determine the load, velocity, and surface disorder dependence of friction. In the two-dimensional model, the single asperity can follow the minimum energy path in wearless regime; however, with increasing load and sliding velocity, the slip-stick movement dominates the dynamic motion and results in an increase in friction by impeding tracing the minimum energy path. Contrary to the two-dimensional model, when the one-dimensional PT model is employed, the single asperity cannot escape to the minimum energy minimum due to constraint motion and reveals only a trivial dependence of friction on load, velocity, and surface disorder. Our computational analyses clarify the physical differences between the predictions of the one-dimensional and two-dimensional models and open new avenues for disordered surfaces for low energy dissipation applications in wearless friction regime.

The ISEE-C plasma wave investigation

NASA Technical Reports Server (NTRS)

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

1978-01-01

The ISEE-C plasma wave investigation is designed to provide comprehensive information on interplanetary wave-particle interactions. Three spectrum analyzers with a total of 19 bandpass channels cover the frequency range 0.3 Hz to 100 kHz. The main analyzer, which uses 16 continuously active amplifiers, gives two complete spectral scans per second in each of 16 filter channels. The instrument sensors include a high-sensitivity magnetic search coil, and electric antennas with effective lengths of 0.6 and 45 m.

On the Ising character of the quantum-phase transition in LiHoF4

NASA Astrophysics Data System (ADS)

Skomski, R.

2016-05-01

It is investigated how a transverse magnetic field affects the quantum-mechanical character of LiHoF4, a system generally considered as a textbook example for an Ising-like quantum-phase transition. In small magnetic fields, the low-temperature behavior of the ions is Ising-like, involving the nearly degenerate low-lying Jz = ± 8 doublet. However, as the transverse field increases, there is a substantial admixture of states having |Jz| < 8. Near the quantum-phase-transition field, the system is distinctively non-Ising like, and all Jz eigenstates yield ground-state contributions of comparable magnitude. A classical analog to this mechanism is the micromagnetic single point in magnets with uniaxial anisotropy. Since Ho3+ has J = 8, the ion's behavior is reminiscent of the classical limit (J = ∞), but quantum corrections remain clearly visible.

Initial survey of the wave distribution functions for plasmaspheric hiss observed by ISEE 1

NASA Technical Reports Server (NTRS)

Storey, L. R. O.; Lefeuvre, F.; Parrot, M.; Cairo, L.; Anderson, R. R.

1991-01-01

The generation mechanism of hiss observed by ISEE 1 satellite in the earth magnetosphere is investigated by analyzing the ELF/VLF wave data obtained from four passes of ISEE 1, all of which occurring during magnetically quiet periods. The results of these measurements, together with those published earlier, indicate that the generation mechanisms proposed by Kennel alnd Petschek (1966), by Thorne et al. (1979), and by Solomon et al. (1988, 1989) are all physically possible and can come into action whenever the necessary conditions exist. However, plasmaspheric hiss was observed by ISEE even when the conditions for any of these mechanisms existed; under these conditions, hiss appears to be generated near the equatorial plane over a wide range of L values, with the wave normals at large angles to the field. The generation mechanism that applies in such cases is still unknown.

Criticality of the random field Ising model in and out of equilibrium: A nonperturbative functional renormalization group description

NASA Astrophysics Data System (ADS)

Balog, Ivan; Tarjus, Gilles; Tissier, Matthieu

2018-03-01

We show that, contrary to previous suggestions based on computer simulations or erroneous theoretical treatments, the critical points of the random-field Ising model out of equilibrium, when quasistatically changing the applied source at zero temperature, and in equilibrium are not in the same universality class below some critical dimension dD R≈5.1 . We demonstrate this by implementing a nonperturbative functional renormalization group for the associated dynamical field theory. Above dD R, the avalanches, which characterize the evolution of the system at zero temperature, become irrelevant at large distance, and hysteresis and equilibrium critical points are then controlled by the same fixed point. We explain how to use computer simulation and finite-size scaling to check the correspondence between in and out of equilibrium criticality in a far less ambiguous way than done so far.

High-Precision Monte Carlo Simulation of the Ising Models on the Penrose Lattice and the Dual Penrose Lattice

NASA Astrophysics Data System (ADS)

Komura, Yukihiro; Okabe, Yutaka

2016-04-01

We study the Ising models on the Penrose lattice and the dual Penrose lattice by means of the high-precision Monte Carlo simulation. Simulating systems up to the total system size N = 20633239, we estimate the critical temperatures on those lattices with high accuracy. For high-speed calculation, we use the generalized method of the single-GPU-based computation for the Swendsen-Wang multi-cluster algorithm of Monte Carlo simulation. As a result, we estimate the critical temperature on the Penrose lattice as Tc/J = 2.39781 ± 0.00005 and that of the dual Penrose lattice as Tc*/J = 2.14987 ± 0.00005. Moreover, we definitely confirm the duality relation between the critical temperatures on the dual pair of quasilattices with a high degree of accuracy, sinh (2J/Tc)sinh (2J/Tc*) = 1.00000 ± 0.00004.

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

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.

Parallel tempering simulation of the three-dimensional Edwards-Anderson model with compact asynchronous multispin coding on GPU

NASA Astrophysics Data System (ADS)

Fang, Ye; Feng, Sheng; Tam, Ka-Ming; Yun, Zhifeng; Moreno, Juana; Ramanujam, J.; Jarrell, Mark

2014-10-01

Monte Carlo simulations of the Ising model play an important role in the field of computational statistical physics, and they have revealed many properties of the model over the past few decades. However, the effect of frustration due to random disorder, in particular the possible spin glass phase, remains a crucial but poorly understood problem. One of the obstacles in the Monte Carlo simulation of random frustrated systems is their long relaxation time making an efficient parallel implementation on state-of-the-art computation platforms highly desirable. The Graphics Processing Unit (GPU) is such a platform that provides an opportunity to significantly enhance the computational performance and thus gain new insight into this problem. In this paper, we present optimization and tuning approaches for the CUDA implementation of the spin glass simulation on GPUs. We discuss the integration of various design alternatives, such as GPU kernel construction with minimal communication, memory tiling, and look-up tables. We present a binary data format, Compact Asynchronous Multispin Coding (CAMSC), which provides an additional 28.4% speedup compared with the traditionally used Asynchronous Multispin Coding (AMSC). Our overall design sustains a performance of 33.5 ps per spin flip attempt for simulating the three-dimensional Edwards-Anderson model with parallel tempering, which significantly improves the performance over existing GPU implementations.

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 Ca

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

Magnetization plateaus and ground-state phase diagrams of the S=1 Ising model on the Shastry Sutherland lattice

NASA Astrophysics Data System (ADS)

Deviren, Seyma Akkaya

2017-02-01

In this research, we have investigated the magnetic properties of the spin-1 Ising model on the Shastry Sutherland lattice with the crystal field interaction by using the effective-field theory with correlations. The effects of the applied field on the magnetization are examined in detail in order to obtain the magnetization plateaus, thus different types of magnetization plateaus, such as 1/4, 1/3, 1/2, 3/5, 2/3 and 7/9 of the saturation, are obtained for strong enough magnetic fields (h). Magnetization plateaus exhibit single, triple, quintuplet and sextuple forms according to the interaction parameters, hence the magnetization plateaus originate from the competition between the crystal field (D) and exchange interaction parameters (J, J‧). The ground-state phase diagrams of the system are presented in three varied planes, namely (h/J, J‧/J), (h/J, D/J) and (D/J, J‧/J) planes. These phase diagrams display the Néel (N), collinear (C) and ferromagnetic (F) phases for certain values of the model parameters. The obtained results are in good agreement with some theoretical and experimental studies.

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions.

PubMed

Fytas, Nikolaos G; Martín-Mayor, Víctor

2016-06-01

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.227201] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero- and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent α of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

Improved belief propagation algorithm finds many Bethe states in the random-field Ising model on random graphs

NASA Astrophysics Data System (ADS)

Perugini, G.; Ricci-Tersenghi, F.

2018-01-01

We first present an empirical study of the Belief Propagation (BP) algorithm, when run on the random field Ising model defined on random regular graphs in the zero temperature limit. We introduce the notion of extremal solutions for the BP equations, and we use them to fix a fraction of spins in their ground state configuration. At the phase transition point the fraction of unconstrained spins percolates and their number diverges with the system size. This in turn makes the associated optimization problem highly non trivial in the critical region. Using the bounds on the BP messages provided by the extremal solutions we design a new and very easy to implement BP scheme which is able to output a large number of stable fixed points. On one hand this new algorithm is able to provide the minimum energy configuration with high probability in a competitive time. On the other hand we found that the number of fixed points of the BP algorithm grows with the system size in the critical region. This unexpected feature poses new relevant questions about the physics of this class of models.

Study on the Ising Antiferromagnet in an External Magnetic Field

NASA Astrophysics Data System (ADS)

Kim, Seung-Yeon

2018-06-01

In an external magnetic field, the properties of an antiferromagnet are much less well understood than those of a ferromagnet are. An abnormal peak in the specific heat of matter at a low temperature, the so-called Schottky anomaly, is one of the most universal phenomena, and it is the most important concept in studying experimentally the low-energy structure of matter. We investigate the unknown properties of the Ising antiferromagnet in an external magnetic field B, in particular, the magnetic-field dependence of the Schottky anomaly of the Ising antiferromagnet systematically. We find three different kinds of Schottky anomalies for the Ising antiferromagnet. First, for B > B c , where B c is the critical magnetic field, both the maximum of the Schottky anomaly C s ( B) and the Schottky temperature T s ( B) increase as B increases. In particular, T s ( B) follows T s ( B) = 0.8336( B - B c ) only for B > B c . Second, for B < B c , both the maximum of the Schottky anomaly and the Schottky temperature decrease as B increases, in clear contrast to the increasing behaviors of the Schottky anomaly for B > B c . Third, at B = B c , the unusual Schottky anomaly appears due to the nonzero ground-state entropy, similar to real ice and spin glass. We expect that our results will play a vital role in measuring and understanding the properties of an antiferromagnet and related materials in an external magnetic field.

Magnetoanisotropic spin-triplet Andreev reflection in ferromagnet-Ising superconductor junctions

NASA Astrophysics Data System (ADS)

Lv, Peng; Zhou, Yan-Feng; Yang, Ning-Xuan; Sun, Qing-Feng

2018-04-01

We theoretically study the electronic transport through a ferromagnet-Ising superconductor junction. A tight-binding Hamiltonian describing the Ising superconductor is presented. Then by combining the nonequilibrium Green's function method, the expressions of Andreev reflection coefficient and conductance are obtained. A strong magnetoanisotropic spin-triplet Andreev reflection is shown, and the magnetoanisotropic period is π instead of 2 π as in the conventional magnetoanisotropic system. We demonstrate a significant increase of the spin-triplet Andreev reflection for the single-band Ising superconductor. Furthermore, the dependence of the Andreev reflection on the incident energy and incident angle are also investigated. A complete Andreev reflection can occur when the incident energy is equal to the superconducting gap, regardless of the Fermi energy (spin polarization) of the ferromagnet. For the suitable oblique incidence, the spin-triplet Andreev reflection can be strongly enhanced. In addition, the conductance spectroscopies of both zero bias and finite bias are studied, and the influence of gate voltage, exchange energy, and spin-orbit coupling on the conductance spectroscopy are discussed in detail. The conductance exhibits a strong magnetoanisotropy with period π as the Andreev reflection coefficient. When the magnetization direction is parallel to the junction plane, a large conductance peak always emerges at the superconducting gap. This work offers a comprehensive and systematic study of the spin-triplet Andreev reflection and has an underlying application of π -periodic spin valve in spintronics.

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.

Finite-size effects for anisotropic 2D Ising model with various boundary conditions

NASA Astrophysics Data System (ADS)

Izmailian, N. Sh

2012-12-01

We analyze the exact partition function of the anisotropic Ising model on finite M × N rectangular lattices under four different boundary conditions (periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa)) obtained by Kaufman (1949 Phys. Rev. 76 1232), Wu and Hu (2002 J. Phys. A: Math. Gen. 35 5189) and Kastening (2002 Phys. Rev. E 66 057103)). We express the partition functions in terms of the partition functions Zα, β(J, k) with (α, β) = (0, 0), (1/2, 0), (0, 1/2) and (1/2, 1/2), J is an interaction coupling and k is an anisotropy parameter. Based on such expressions, we then extend the algorithm of Ivashkevich et al (2002 J. Phys. A: Math. Gen. 35 5543) to derive the exact asymptotic expansion of the logarithm of the partition function for all boundary conditions mentioned above. Our result is f = fbulk + ∑∞p = 0fp(ρ, k)S-p - 1, where f is the free energy of the system, fbulk is the free energy of the bulk, S = MN is the area of the lattice and ρ = M/N is the aspect ratio. All coefficients in this expansion are expressed through analytical functions. We have introduced the effective aspect ratio ρeff = ρ/sinh 2Jc and show that for pp and aa boundary conditions all finite size correction terms are invariant under the transformation ρeff → 1/ρeff. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.

In-Space Engine (ISE-100) Development - Design Verification Test

NASA Technical Reports Server (NTRS)

Trinh, Huu P.; Popp, Chris; Bullard, Brad

2017-01-01

In the past decade, NASA has formulated science mission concepts with an anticipation of landing spacecraft on the lunar surface, meteoroids, and other planets. Advancing thruster technology for spacecraft propulsion systems has been considered for maximizing science payload. Starting in 2010, development of In-Space Engine (designated as ISE-100) has been carried out. ISE-100 thruster is designed based on heritage Missile Defense Agency (MDA) technology aimed for a lightweight and efficient system in terms volume and packaging. It runs with a hypergolic bi-propellant system: MON-25 (nitrogen tetroxide, N2O4, with 25% of nitric oxide, NO) and MMH (monomethylhydrazine, CH6N2) for NASA spacecraft applications. The utilization of this propellant system will provide a propulsion system capable of operating at wide range of temperatures, from 50 C (122 F) down to -30 C (-22 F) to drastically reduce heater power. The thruster is designed to deliver 100 lb(sub f) of thrust with the capability of a pulse mode operation for a wide range of mission duty cycles (MDCs). Two thrusters were fabricated. As part of the engine development, this test campaign is dedicated for the design verification of the thruster. This presentation will report the efforts of the design verification hot-fire test program of the ISE-100 thruster in collaboration between NASA Marshall Space Flight Center (MSFC) and Aerojet Rocketdyne (AR) test teams. The hot-fire tests were conducted at Advance Mobile Propulsion Test (AMPT) facility in Durango, Colorado, from May 13 to June 10, 2016. This presentation will also provide a summary of key points from the test results.

Three-dimensional modeling of tea-shoots using images and models.

PubMed

Wang, Jian; Zeng, Xianyin; Liu, Jianbing

2011-01-01

In this paper, a method for three-dimensional modeling of tea-shoots with images and calculation models is introduced. The process is as follows: the tea shoots are photographed with a camera, color space conversion is conducted, using an improved algorithm that is based on color and regional growth to divide the tea shoots in the images, and the edges of the tea shoots extracted with the help of edge detection; after that, using the divided tea-shoot images, the three-dimensional coordinates of the tea shoots are worked out and the feature parameters extracted, matching and calculation conducted according to the model database, and finally the three-dimensional modeling of tea-shoots is completed. According to the experimental results, this method can avoid a lot of calculations and has better visual effects and, moreover, performs better in recovering the three-dimensional information of the tea shoots, thereby providing a new method for monitoring the growth of and non-destructive testing of tea shoots.

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.).

Dynamic colloidal assembly pathways via low dimensional models

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

Yang, Yuguang; Bevan, Michael A., E-mail: mabevan@jhu.edu; Thyagarajan, Raghuram

2016-05-28

Here we construct a low-dimensional Smoluchowski model for electric field mediated colloidal crystallization using Brownian dynamic simulations, which were previously matched to experiments. Diffusion mapping is used to infer dimensionality and confirm the use of two order parameters, one for degree of condensation and one for global crystallinity. Free energy and diffusivity landscapes are obtained as the coefficients of a low-dimensional Smoluchowski equation to capture the thermodynamics and kinetics of microstructure evolution. The resulting low-dimensional model quantitatively captures the dynamics of different assembly pathways between fluid, polycrystal, and single crystals states, in agreement with the full N-dimensional data as characterizedmore » by first passage time distributions. Numerical solution of the low-dimensional Smoluchowski equation reveals statistical properties of the dynamic evolution of states vs. applied field amplitude and system size. The low-dimensional Smoluchowski equation and associated landscapes calculated here can serve as models for predictive control of electric field mediated assembly of colloidal ensembles into two-dimensional crystalline objects.« less

The ISES: A non-intrusive medium for in-space experiments in on-board information extraction

NASA Technical Reports Server (NTRS)

Murray, Nicholas D.; Katzberg, Stephen J.; Nealy, Mike

1990-01-01

The Information Science Experiment System (ISES) represents a new approach in applying advanced systems technology and techniques to on-board information extraction in the space environment. Basically, what is proposed is a 'black box' attached to the spacecraft data bus or local area network. To the spacecraft the 'black box' appears to be just another payload requiring power, heat rejection, interfaces, adding weight, and requiring time on the data management and communication system. In reality, the 'black box' is a programmable computational resource which eavesdrops on the data network, taking and producing selectable, real-time science data back on the network. This paper will present a brief overview of the ISES Concept and will discuss issues related to applying the ISES to the polar platform and Space Station Freedom. Critical to the operation of ISES is the viability of a payload-like interface to the spacecraft data bus or local area network. Study results that address this question will be reviewed vis-a-vis the solar platform and the core space station. Also, initial results of processing science and other requirements for onboard, real-time information extraction will be presented with particular emphasis on the polar platform. Opportunities for a broader range of applications on the core space station will also be discussed.

Continuum modeling of three-dimensional truss-like space structures

NASA Technical Reports Server (NTRS)

Nayfeh, A. H.; Hefzy, M. S.

1978-01-01

A mathematical and computational analysis capability has been developed for calculating the effective mechanical properties of three-dimensional periodic truss-like structures. Two models are studied in detail. The first, called the octetruss model, is a three-dimensional extension of a two-dimensional model, and the second is a cubic model. Symmetry considerations are employed as a first step to show that the specific octetruss model has four independent constants and that the cubic model has two. The actual values of these constants are determined by averaging the contributions of each rod element to the overall structure stiffness. The individual rod member contribution to the overall stiffness is obtained by a three-dimensional coordinate transformation. The analysis shows that the effective three-dimensional elastic properties of both models are relatively close to each other.

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.

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.

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.

Frustrated spin-1/2 Ising antiferromagnet on a square lattice in a transverse field

NASA Astrophysics Data System (ADS)

Bobák, A.; Jurčišinová, E.; Jurčišin, M.; Žukovič, M.

2018-02-01

We investigate the phase transitions and tricritical behaviors of the frustrated Ising antiferromagnet with first- (J1<0 ) and second- (J2<0 ) nearest-neighbor interactions in a transverse field Ω on the square lattice using an effective-field theory with correlations based on a single-spin approximation. We have proposed a functional for the free energy to obtain the phase diagram in the T -R (R =J2/|J1| ) or T -Ω planes. It is shown that due to the transverse field the phase transition between ordered and disordered phases changes in the tricritical point (TCP) from the second order to the first order. The longitudinal and transverse magnetizations are also studied for selected values of R and Ω . In particular, the variation of TCP at the ground state in the three-dimensional space is constructed. For some special cases, values of the critical temperature and the critical transverse field have been determined analytically.

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.

Dynamo transition in low-dimensional models.

PubMed

Verma, Mahendra K; Lessinnes, Thomas; Carati, Daniele; Sarris, Ioannis; Kumar, Krishna; Singh, Meenakshi

2008-09-01

Two low-dimensional magnetohydrodynamic models containing three velocity and three magnetic modes are described. One of them (nonhelical model) has zero kinetic and current helicity, while the other model (helical) has nonzero kinetic and current helicity. The velocity modes are forced in both these models. These low-dimensional models exhibit a dynamo transition at a critical forcing amplitude that depends on the Prandtl number. In the nonhelical model, dynamo exists only for magnetic Prandtl number beyond 1, while the helical model exhibits dynamo for all magnetic Prandtl number. Although the model is far from reproducing all the possible features of dynamo mechanisms, its simplicity allows a very detailed study and the observed dynamo transition is shown to bear similarities with recent numerical and experimental results.

Quantum simulations of the Ising model with trapped ions: Devil's staircase and arbitrary lattice proposal

NASA Astrophysics Data System (ADS)

Korenblit, Simcha

A collection of trapped atomic ions represents one of the most attractive platforms for the quantum simulation of interacting spin networks and quantum magnetism. Spin-dependent optical dipole forces applied to an ion crystal create long-range effective spin-spin interactions and allow the simulation of spin Hamiltonians that possess nontrivial phases and dynamics. We trap linear chains of 171Yb+ ions in a Paul trap, and constrain the occupation of energy levels to the ground hyperne clock-states, creating a qubit or pseudo-spin 1/2 system. We proceed to implement spin-spin couplings between two ions using the far detuned Molmer-Sorenson scheme and perform adiabatic quantum simulations of Ising Hamiltonians with long-range couplings. We then demonstrate our ability to control the sign and relative strength of the interaction between three ions. Using this control, we simulate a frustrated triangular lattice, and for the first time establish an experimental connection between frustration and quantum entanglement. We then scale up our simulation to show phase transitions from paramagnetism to ferromagnetism for nine ions, and to anti-ferromagnetism for sixteen ions. The experimental work culminates with our most complicated Hamiltonian---a long range anti-ferromagnetic Ising interaction between 10 ions with a biasing axial field. Theoretical work presented in this thesis shows how the approach to quantum simulation utilized in this thesis can be further extended and improved. It is shown how appropriate design of laser fields can provide for arbitrary multidimensional spin-spin interaction graphs even for the case of a linear spatial array of ions. This scheme uses currently existing trap technology and is scalable to levels where classical methods of simulation are intractable.

Ising universality describes emergent long-range synchronization of coupled ecological oscillators

NASA Astrophysics Data System (ADS)

Noble, Andrew

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. By contrast, recent work shows how scale-invariant synchronization can emerge from locally coupled population dynamics. In particular, we have found that the transition from incoherence to long-range synchronization of coupled ecological two-cycles is described by the Ising universality class. I will discuss evidence that an Ising critical point describes long-range correlations found in data on the individual yields of female pistachio trees in a large orchard. NSF INSPIRE Grant No. 1344187.

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.

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.

Data reduction and analysis of ISEE magnetometer experiment

NASA Technical Reports Server (NTRS)

Russell, C. T.

1982-01-01

The ISEE-1 and -2 magnetometer data was reduced. The up and downstream turbulence associated with interplanetary shocks were studied, including methods of determining shock normals, and the similarities and differences in laminar and quasi-laminar shock structure. The associated up and downstream turbulence was emphasized. The distributions of flux transfer events, field aligned currents in the near tail, and substorm dynamics in the magnetotail were also investigated.

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.

Shielding property for thermal equilibrium states in the quantum Ising model

NASA Astrophysics Data System (ADS)

Móller, N. S.; de Paula, A. L.; Drumond, R. C.

2018-03-01

We show that Gibbs states of nonhomogeneous transverse Ising chains satisfy a shielding property. Namely, whatever the fields on each spin and exchange couplings between neighboring spins are, if the field in one particular site is null, then the reduced states of the subchains to the right and to the left of this site are exactly the Gibbs states of each subchain alone. Therefore, even if there is a strong exchange coupling between the extremal sites of each subchain, the Gibbs states of the each subchain behave as if there is no interaction between them. In general, if a lattice can be divided into two disconnected regions separated by an interface of sites with zero applied field, then we can guarantee a similar result only if the surface contains a single site. Already for an interface with two sites we show an example where the property does not hold. When it holds, however, we show that if a perturbation of the Hamiltonian parameters is done in one side of the lattice, then the other side is completely unchanged, with regard to both its equilibrium state and dynamics.

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.

Assessing change of environmental dynamics by legislation in Japan, using red tide occurrence in Ise Bay as an indicator.

PubMed

Suzuki, Chika

2016-01-30

Tokyo Bay, Ise Bay, and the Seto Inland Sea are the total pollutant load control target areas in Japan. A significant correlation between the incidence of red tides and water quality has been observed in the Seto Inland Sea (Honjo, 1991). However, while red tides also occur in Ise Bay and Tokyo Bay, similar correlations have not been observed. Hence, it is necessary to understand what factors cause red tides to effectively manage these semi-closed systems. This study aims to investigate the relationship between the dynamics of the Red Tide Index and nitrogen regulation as well as phosphorus regulation, even in Ise Bay where, unlike Tokyo Bay, there are few observation items, by selecting a suitable objective variable. The introduction of a new technique that uses the Red Tide Index has revealed a possibility that the total pollution load control has influenced the dynamics of red tide blooms in Ise Bay. Copyright © 2015 Elsevier Ltd. All rights reserved.

Modeling Three-Dimensional Flow in Confined Aquifers by Superposition of Both Two- and Three-Dimensional Analytic Functions

NASA Astrophysics Data System (ADS)

Haitjema, Henk M.

1985-10-01

A technique is presented to incorporate three-dimensional flow in a Dupuit-Forchheimer model. The method is based on superposition of approximate analytic solutions to both two- and three-dimensional flow features in a confined aquifer of infinite extent. Three-dimensional solutions are used in the domain of interest, while farfield conditions are represented by two-dimensional solutions. Approximate three- dimensional solutions have been derived for a partially penetrating well and a shallow creek. Each of these solutions satisfies the condition that no flow occurs across the confining layers of the aquifer. Because of this condition, the flow at some distance of a three-dimensional feature becomes nearly horizontal. Consequently, remotely from a three-dimensional feature, its three-dimensional solution is replaced by a corresponding two-dimensional one. The latter solution is trivial as compared to its three-dimensional counterpart, and its use greatly enhances the computational efficiency of the model. As an example, the flow is modeled between a partially penetrating well and a shallow creek that occur in a regional aquifer system.

Two-dimensional lattice Boltzmann model for magnetohydrodynamics.

PubMed

Schaffenberger, Werner; Hanslmeier, Arnold

2002-10-01

We present a lattice Boltzmann model for the simulation of two-dimensional magnetohydro dynamic (MHD) flows. The model is an extension of a hydrodynamic lattice Boltzman model with 9 velocities on a square lattice resulting in a model with 17 velocities. Earlier lattice Boltzmann models for two-dimensional MHD used a bidirectional streaming rule. However, the use of such a bidirectional streaming rule is not necessary. In our model, the standard streaming rule is used, allowing smaller viscosities. To control the viscosity and the resistivity independently, a matrix collision operator is used. The model is then applied to the Hartmann flow, giving reasonable results.

Magnetic and magnetocaloric properties of the exactly solvable mixed-spin Ising model on a decorated triangular lattice in a magnetic field

NASA Astrophysics Data System (ADS)

Gálisová, Lucia; Strečka, Jozef

2018-05-01

The ground state, zero-temperature magnetization process, critical behaviour and isothermal entropy change of the mixed-spin Ising model on a decorated triangular lattice in a magnetic field are exactly studied after performing the generalized decoration-iteration mapping transformation. It is shown that both the inverse and conventional magnetocaloric effect can be found near the absolute zero temperature. The former phenomenon can be found in a vicinity of the discontinuous phase transitions and their crossing points, while the latter one occurs in some paramagnetic phases due to a spin frustration to be present at zero magnetic field. The inverse magnetocaloric effect can also be detected slightly above continuous phase transitions following the power-law dependence | - ΔSisomin | ∝hn, where n depends basically on the ground-state spin ordering.

Comparison of two-dimensional and quasi-one-dimensional scramjet models by the example of VAG experiment

NASA Astrophysics Data System (ADS)

Seleznev, R. K.

2017-02-01

In the paper two-dimensional and quasi-one dimensional models for scramjet combustion chamber are described. Comparison of the results of calculations for the two-dimensional and quasi-one dimensional code by the example of VAG experiment are presented.

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.

The ISEE-3 ULEWAT: Flux tape description and heavy ion fluxes 1978-1984. [plasma diagnostics

NASA Technical Reports Server (NTRS)

Mason, G. M.; Klecker, B.

1985-01-01

The ISEE ULEWAT FLUX tapes contain ULEWAT and ISEE pool tape data summarized over relatively long time intervals (1hr) in order to compact the data set into an easily usable size. (Roughly 3 years of data fit onto one 1600 BPI 9-track magnetic tape). In making the tapes, corrections were made to the ULEWAT basic data tapes in order to, remove rate spikes and account for changes in instrument response so that to a large extent instrument fluxes can be calculated easily from the FLUX tapes without further consideration of instrument performance.

Spin dynamics of random Ising chain in coexisting transverse and longitudinal magnetic fields

NASA Astrophysics Data System (ADS)

Liu, Zhong-Qiang; Jiang, Su-Rong; Kong, Xiang-Mu; Xu, Yu-Liang

2017-05-01

The dynamics of the random Ising spin chain in coexisting transverse and longitudinal magnetic fields is studied by the recursion method. Both the spin autocorrelation function and its spectral density are investigated by numerical calculations. It is found that system's dynamical behaviors depend on the deviation σJ of the random exchange coupling between nearest-neighbor spins and the ratio rlt of the longitudinal and the transverse fields: (i) For rlt = 0, the system undergoes two crossovers from N independent spins precessing about the transverse magnetic field to a collective-mode behavior, and then to a central-peak behavior as σJ increases. (ii) For rlt ≠ 0, the system may exhibit a coexistence behavior of a collective-mode one and a central-peak one. When σJ is small (or large enough), system undergoes a crossover from a coexistence behavior (or a disordered behavior) to a central-peak behavior as rlt increases. (iii) Increasing σJ depresses effects of both the transverse and the longitudinal magnetic fields. (iv) Quantum random Ising chain in coexisting magnetic fields may exhibit under-damping and critical-damping characteristics simultaneously. These results indicate that changing the external magnetic fields may control and manipulate the dynamics of the random Ising chain.

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.

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.

Dimensionality reduction in epidemic spreading models

NASA Astrophysics Data System (ADS)

Frasca, M.; Rizzo, A.; Gallo, L.; Fortuna, L.; Porfiri, M.

2015-09-01

Complex dynamical systems often exhibit collective dynamics that are well described by a reduced set of key variables in a low-dimensional space. Such a low-dimensional description offers a privileged perspective to understand the system behavior across temporal and spatial scales. In this work, we propose a data-driven approach to establish low-dimensional representations of large epidemic datasets by using a dimensionality reduction algorithm based on isometric features mapping (ISOMAP). We demonstrate our approach on synthetic data for epidemic spreading in a population of mobile individuals. We find that ISOMAP is successful in embedding high-dimensional data into a low-dimensional manifold, whose topological features are associated with the epidemic outbreak. Across a range of simulation parameters and model instances, we observe that epidemic outbreaks are embedded into a family of closed curves in a three-dimensional space, in which neighboring points pertain to instants that are close in time. The orientation of each curve is unique to a specific outbreak, and the coordinates correlate with the number of infected individuals. A low-dimensional description of epidemic spreading is expected to improve our understanding of the role of individual response on the outbreak dynamics, inform the selection of meaningful global observables, and, possibly, aid in the design of control and quarantine procedures.

Rigorous proof for the nonlocal correlation function in the transverse Ising model with ring frustration.

PubMed

Dong, Jian-Jun; Zheng, Zhen-Yu; Li, Peng

2018-01-01

An unusual correlation function was conjectured by Campostrini et al. [Phys. Rev. E 91, 042123 (2015)PLEEE81539-375510.1103/PhysRevE.91.042123] for the ground state of a transverse Ising chain with geometrical frustration. Later, we provided a rigorous proof for it and demonstrated its nonlocal nature based on an evaluation of a Toeplitz determinant in the thermodynamic limit [J. Stat. Mech. (2016) 11310210.1088/1742-5468/2016/11/113102]. In this paper, we further prove that all the low excited energy states forming the gapless kink phase share the same asymptotic correlation function with the ground state. As a consequence, the thermal correlation function almost remains constant at low temperatures if one assumes a canonical ensemble.

Frustrated ground state in the metallic Ising antiferromagnet Nd2Ni2In

NASA Astrophysics Data System (ADS)

Sala, G.; Mašková, S.; Stone, M. B.

2017-10-01

We used inelastic neutron scattering measurements to examine the intermetallic Ising antiferromagnet Nd2Ni2In . The dynamical structure factor displays a spectrum with multiple crystal field excitations. These crystal field excitations consist of a set of four transitions covering a range of energies between 4 and 80 meV. The spectrum is very sensitive to the temperature, and we observed a softening and a shift in the energies above the transition temperature of the system. The analysis of the crystalline electric field scheme confirms the Ising nature of the spins and their orientation as proposed by previous studies. We characterized Nd2Ni2In as a large moment intermetallic antiferromagnet with the potential to support a geometrically frustrated Shastry-Sutherland lattice.

Minimizers with Bounded Action for the High-Dimensional Frenkel-Kontorova Model

NASA Astrophysics Data System (ADS)

Miao, Xue-Qing; Wang, Ya-Nan; Qin, Wen-Xin

In Aubry-Mather theory for monotone twist maps or for one-dimensional Frenkel-Kontorova (FK) model with nearest neighbor interactions, each global minimizer (minimal energy configuration) is naturally Birkhoff. However, this is not true for the one-dimensional FK model with non-nearest neighbor interactions or for the high-dimensional FK model. In this paper, we study the Birkhoff property of minimizers with bounded action for the high-dimensional FK model.

Variational asymptotic modeling of composite dimensionally reducible structures

NASA Astrophysics Data System (ADS)

Yu, Wenbin

A general framework to construct accurate reduced models for composite dimensionally reducible structures (beams, plates and shells) was formulated based on two theoretical foundations: decomposition of the rotation tensor and the variational asymptotic method. Two engineering software systems, Variational Asymptotic Beam Sectional Analysis (VABS, new version) and Variational Asymptotic Plate and Shell Analysis (VAPAS), were developed. Several restrictions found in previous work on beam modeling were removed in the present effort. A general formulation of Timoshenko-like cross-sectional analysis was developed, through which the shear center coordinates and a consistent Vlasov model can be obtained. Recovery relations are given to recover the asymptotic approximations for the three-dimensional field variables. A new version of VABS has been developed, which is a much improved program in comparison to the old one. Numerous examples are given for validation. A Reissner-like model being as asymptotically correct as possible was obtained for composite plates and shells. After formulating the three-dimensional elasticity problem in intrinsic form, the variational asymptotic method was used to systematically reduce the dimensionality of the problem by taking advantage of the smallness of the thickness. The through-the-thickness analysis is solved by a one-dimensional finite element method to provide the stiffnesses as input for the two-dimensional nonlinear plate or shell analysis as well as recovery relations to approximately express the three-dimensional results. The known fact that there exists more than one theory that is asymptotically correct to a given order is adopted to cast the refined energy into a Reissner-like form. A two-dimensional nonlinear shell theory consistent with the present modeling process was developed. The engineering computer code VAPAS was developed and inserted into DYMORE to provide an efficient and accurate analysis of composite plates and

Applications of ISES for the atmospheric sciences

NASA Technical Reports Server (NTRS)

Hoell, James M., Jr.

1990-01-01

The proposed Information Sciences Experiment System (ISES) will offer the opportunity for real-time access to measurements acquired aboard the Earth Observation System (Eos) satellite. These measurements can then be transmitted to remotely located ground based stations. The application of such measurements to issues related to atmospheric science which was presented to a workshop convened to review possible application of the ISES in earth sciences is summarized. The proposed protocol for Eos instruments requires that measurement results be available in a central data archive within 72 hours of acquiring data. Such a turnaround of raw satellite data to the final product will clearly enhance the timeliness of the results. Compared to the time that results from many current satellite programs, the 72 hour turnaround may be considered real time. Examples are discussed showing how real-time measurements from one or more of the proposed Eos instruments could have been applied to the study of certain issues important to global atmospheric chemistry. Each of the examples discussed is based upon a field mission conducted during the past five years. Each of these examples will emphasize how real-time data could have been used to alter the course of a field experiment, thereby enhancing the scientific output. For the examples, brief overviews of the scientific rationale and objectives, the region of operation, the measurements aboard the aircraft, and finally how one or more of the proposed Eos instruments could have provided data to enhance the productivity of the mission are discussed.

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.

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.

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 modeling of the plasma arc in arc welding

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

Xu, G.; Tsai, H. L.; Hu, J.

2008-11-15

Most previous three-dimensional modeling on gas tungsten arc welding (GTAW) and gas metal arc welding (GMAW) focuses on the weld pool dynamics and assumes the two-dimensional axisymmetric Gaussian distributions for plasma arc pressure and heat flux. In this article, a three-dimensional plasma arc model is developed, and the distributions of velocity, pressure, temperature, current density, and magnetic field of the plasma arc are calculated by solving the conservation equations of mass, momentum, and energy, as well as part of the Maxwell's equations. This three-dimensional model can be used to study the nonaxisymmetric plasma arc caused by external perturbations such asmore » an external magnetic field. It also provides more accurate boundary conditions when modeling the weld pool dynamics. The present work lays a foundation for true three-dimensional comprehensive modeling of GTAW and GMAW including the plasma arc, weld pool, and/or electrode.« less

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.

A three-dimensional model of Tangential YORP

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

Golubov, O.; Scheeres, D. J.; Krugly, Yu. N., E-mail: golubov@astron.kharkov.ua

2014-10-10

Tangential YORP, or TYORP, has recently been demonstrated to be an important factor in the evolution of an asteroid's rotation state. It is complementary to normal YORP, or NYORP, which used to be considered previously. While NYORP is produced by non-symmetry in the large-scale geometry of an asteroid, TYORP is due to heat conductivity in stones on the surface of the asteroid. To date, TYORP has been studied only in a simplified one-dimensional model, substituting stones with high long walls. This article for the first time considers TYORP in a realistic three-dimensional model, also including shadowing and self-illumination effects viamore » ray tracing. TYORP is simulated for spherical stones lying on regolith. The model includes only five free parameters and the dependence of the TYORP on each of them is studied. The TYORP torque appears to be smaller than previous estimates from the one-dimensional model, but is still comparable to the NYORP torques. These results can be used to estimate TYORP of different asteroids and also as a basis for more sophisticated models of TYORP.« less

Phase transitions and thermal entanglement of the distorted Ising-Heisenberg spin chain: topology of multiple-spin exchange interactions in spin ladders

NASA Astrophysics Data System (ADS)

Arian Zad, Hamid; Ananikian, Nerses

2017-11-01

We consider a symmetric spin-1/2 Ising-XXZ double sawtooth spin ladder obtained from distorting a spin chain, with the XXZ interaction between the interstitial Heisenberg dimers (which are connected to the spins based on the legs via an Ising-type interaction), the Ising coupling between nearest-neighbor spins of the legs and rungs spins, respectively, and additional cyclic four-spin exchange (ring exchange) in the square plaquette of each block. The presented analysis supplemented by results of the exact solution of the model with infinite periodic boundary implies a rich ground state phase diagram. As well as the quantum phase transitions, the characteristics of some of the thermodynamic parameters such as heat capacity, magnetization and magnetic susceptibility are investigated. We prove here that among the considered thermodynamic and thermal parameters, solely heat capacity is sensitive versus the changes of the cyclic four-spin exchange interaction. By using the heat capacity function, we obtain a singularity relation between the cyclic four-spin exchange interaction and the exchange coupling between pair spins on each rung of the spin ladder. All thermal and thermodynamic quantities under consideration should be investigated by regarding those points which satisfy the singularity relation. The thermal entanglement within the Heisenberg spin dimers is investigated by using the concurrence, which is calculated from a relevant reduced density operator in the thermodynamic limit.

Underwater striling engine design with modified one-dimensional model

NASA Astrophysics Data System (ADS)

Li, Daijin; Qin, Kan; Luo, Kai

2015-09-01

Stirling engines are regarded as an efficient and promising power system for underwater devices. Currently, many researches on one-dimensional model is used to evaluate thermodynamic performance of Stirling engine, but in which there are still some aspects which cannot be modeled with proper mathematical models such as mechanical loss or auxiliary power. In this paper, a four-cylinder double-acting Stirling engine for Unmanned Underwater Vehicles (UUVs) is discussed. And a one-dimensional model incorporated with empirical equations of mechanical loss and auxiliary power obtained from experiments is derived while referring to the Stirling engine computer model of National Aeronautics and Space Administration (NASA). The P-40 Stirling engine with sufficient testing results from NASA is utilized to validate the accuracy of this one-dimensional model. It shows that the maximum error of output power of theoretical analysis results is less than 18% over testing results, and the maximum error of input power is no more than 9%. Finally, a Stirling engine for UUVs is designed with Schmidt analysis method and the modified one-dimensional model, and the results indicate this designed engine is capable of showing desired output power.

One-Dimensional Modelling of Internal Ballistics

NASA Astrophysics Data System (ADS)

Monreal-González, G.; Otón-Martínez, R. A.; Velasco, F. J. S.; García-Cascáles, J. R.; Ramírez-Fernández, F. J.

2017-10-01

A one-dimensional model is introduced in this paper for problems of internal ballistics involving solid propellant combustion. First, the work presents the physical approach and equations adopted. Closure relationships accounting for the physical phenomena taking place during combustion (interfacial friction, interfacial heat transfer, combustion) are deeply discussed. Secondly, the numerical method proposed is presented. Finally, numerical results provided by this code (UXGun) are compared with results of experimental tests and with the outcome from a well-known zero-dimensional code. The model provides successful results in firing tests of artillery guns, predicting with good accuracy the maximum pressure in the chamber and muzzle velocity what highlights its capabilities as prediction/design tool for internal ballistics.

Surrogate modelling for the prediction of spatial fields based on simultaneous dimensionality reduction of high-dimensional input/output spaces.

PubMed

Crevillén-García, D

2018-04-01

Time-consuming numerical simulators for solving groundwater flow and dissolution models of physico-chemical processes in deep aquifers normally require some of the model inputs to be defined in high-dimensional spaces in order to return realistic results. Sometimes, the outputs of interest are spatial fields leading to high-dimensional output spaces. Although Gaussian process emulation has been satisfactorily used for computing faithful and inexpensive approximations of complex simulators, these have been mostly applied to problems defined in low-dimensional input spaces. In this paper, we propose a method for simultaneously reducing the dimensionality of very high-dimensional input and output spaces in Gaussian process emulators for stochastic partial differential equation models while retaining the qualitative features of the original models. This allows us to build a surrogate model for the prediction of spatial fields in such time-consuming simulators. We apply the methodology to a model of convection and dissolution processes occurring during carbon capture and storage.

Comparisons between thermodynamic and one-dimensional combustion models of spark-ignition engines

NASA Technical Reports Server (NTRS)

Ramos, J. I.

1986-01-01

Results from a one-dimensional combustion model employing a constant eddy diffusivity and a one-step chemical reaction are compared with those of one-zone and two-zone thermodynamic models to study the flame propagation in a spark-ignition engine. One-dimensional model predictions are found to be very sensitive to the eddy diffusivity and reaction rate data. The average mixing temperature found using the one-zone thermodynamic model is higher than those of the two-zone and one-dimensional models during the compression stroke, and that of the one-dimensional model is higher than those predicted by both thermodynamic models during the expansion stroke. The one-dimensional model is shown to predict an accelerating flame even when the front approaches the cold cylinder wall.

Numerical Modeling of Three-Dimensional Confined Flows

NASA Technical Reports Server (NTRS)

Greywall, M. S.

1981-01-01

A three dimensional confined flow model is presented. The flow field is computed by calculating velocity and enthalpy along a set of streamlines. The finite difference equations are obtained by applying conservation principles to streamtubes constructed around the chosen streamlines. With appropriate substitutions for the body force terms, the approach computes three dimensional magnetohydrodynamic channel flows. A listing of a computer code, based on this approach is presented in FORTRAN IV language. The code computes three dimensional compressible viscous flow through a rectangular duct, with the duct cross section specified along the axis.

Dimensional models of personality: the five-factor model and the DSM-5

PubMed Central

Trull, Timothy J.; Widiger, Thomas A.

2013-01-01

It is evident that the classification of personality disorder is shifting toward a dimensional trait model and, more specifically, the five-factor model (FFM). The purpose of this paper is to provide an overview of the FFM of personality disorder. It will begin with a description of this dimensional model of normal and abnormal personality functioning, followed by a comparison with a proposal for future revisions to DSM-5 and a discussion of its potential advantages as an integrative hierarchical model of normal and abnormal personality structure. PMID:24174888

Limit Properties of One Dimensional Periodic Hopping Model

NASA Astrophysics Data System (ADS)

Zhang, Yun-xin

2010-02-01

One dimensional periodic hopping model is useful to understand the motion of microscopic particles in thermal noise environment. In this research, by formal calculation and based on detailed balance, the explicit expressions of the limits of mean velocity and diffusion constant of this model as the number of internal mechanochemical sates tend to infinity are obtained. These results will be helpful to understand the limit of the one dimensional hopping model. At the same time, the work can be used to get more useful results in continuous form from the corresponding ones obtained by discrete models.

Thermodynamics of alternate Ising chains of spins 1 and 3/2 with dipolar, biquadratic, and single ion interactions

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

Fireman, E.C.; dos Santos, R.J.

1997-04-01

Within a recently developed extended decoration-transformation formalism we study the thermodynamic properties of a linear chain of alternate Ising {sigma}=1 and S=3/2 spins. We allow for different anisotropy fields on each subchain of different spins. For some range of the parameter space we show the existence of a crossover from a ferromagnetic to an antiferromagnetic-like behavior of the model, as explicitly captured in the susceptibility results. {copyright} {ital 1997 American Institute of Physics.}

The Conversational Framework and the ISE "Basketball Shot" Video Analysis Activity

ERIC Educational Resources Information Center

English, Vincent; Crotty, Yvonne; Farren, Margaret

2015-01-01

Inspiring Science Education (ISE) (http://www.inspiringscience.eu/) is an EU funded initiative that seeks to further the use of inquiry-based science learning (IBSL) through the medium of ICT in the classroom. The Basketball Shot is a scenario (lesson plan) that involves the use of video capture to help the student investigate the concepts of…

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.

Low-Dimensional Model of a Cylinder Wake

NASA Astrophysics Data System (ADS)

Luchtenburg, Mark; Cohen, Kelly; Siegel, Stefan; McLaughlin, Tom

2003-11-01

In a two-dimensional cylinder wake, self-excited oscillations in the form of periodic shedding of vortices are observed above a critical Reynolds number of about 47. These flow-induced non-linear oscillations lead to some undesirable effects associated with unsteady pressures such as fluid-structure interactions. An effective way of suppressing the self-excited flow oscillations is by the incorporation of closed-loop flow control. In this effort, a low dimensional, proper orthogonal decomposition (POD) model is based on data obtained from direct numerical simulations of the Navier Stokes equations for the two dimensional circular cylinder wake at a Reynolds number of 100. Three different conditions are examined, namely, the unforced wake experiencing steady-state vortex shedding, the transient behavior of the unforced wake at the startup of the simulation, and transient response to open-loop harmonic forcing by translation. We discuss POD mode selection and the number of modes that need to be included in the low-dimensional model. It is found that the transient dynamics need to be represented by a coupled system that includes an aperiodic mean-flow mode, an aperiodic shift mode and the periodic von Karman modes. Finally, a least squares mapping method is introduced to develop the non-linear state equations. The predictive capability of the state equations demonstrates the ability of the above approach to model the transient dynamics of the wake.

Use of the thin sheath approximation for obtaining ion temperatures from the ISEE 1 limited aperture RPA. [for magnetosphere

NASA Technical Reports Server (NTRS)

Comfort, R. H.; Baugher, C. R.; Chappell, C. R.

1982-01-01

A procedure for analyzing low-energy (less than approximately 100 eV) ion data from the plasma composition experiment on ISEE 1 is set forth. The method is based on a derived analytic expression for particle flux to a limited aperture retarding potential analyzer (RPA) in the thin sheath approximation, which makes allowance for some effects of a charged spacecraft on plasma particle trajectories. Calculations using simulated data are employed in testing the efficacy and accuracy of the technique. On the basis of an analysis of these calculation results and the mathematical model, the method is seen as being able to provide accurate ion temperatures from all good plasmaspheric RPA data. It is noted that corresponding densities and spacecraft potentials should be accurate when spacecraft potentials are negative but that they are subject to error for positive spacecraft potentials, particularly when ion Mach numbers are much less than 1. An analysis of data from a representative ISEE 1 pass produces a plasmasphere temperature profile that is consistent in overall structure with previous observations.

Fortuin-Kasteleyn and damage-spreading transitions in random-bond Ising lattices

NASA Astrophysics Data System (ADS)

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

2012-10-01

The Fortuin-Kasteleyn and heat-bath damage-spreading temperatures TFK(p) and TDS(p) are studied on random-bond Ising models of dimensions 2-5 and as functions of the ferromagnetic interaction probability p; the conjecture that TDS(p)˜TFK(p) is tested. It follows from a statement by Nishimori that in any such system, exact coordinates can be given for the intersection point between the Fortuin-Kasteleyn TFK(p) transition line and the Nishimori line [pNL,FK,TNL,FK]. There are no finite-size corrections for this intersection point. In dimension 3, at the intersection concentration [pNL,FK], the damage spreading TDS(p) is found to be equal to TFK(p) to within 0.1%. For the other dimensions, however, TDS(p) is observed to be systematically a few percent lower than TFK(p).

Heat capacity peak at the quantum critical point of the transverse Ising magnet CoNb2O6

PubMed Central

Liang, Tian; Koohpayeh, S. M.; Krizan, J. W.; McQueen, T. M.; Cava, R. J.; Ong, N. P.

2015-01-01

The transverse Ising magnet Hamiltonian describing the Ising chain in a transverse magnetic field is the archetypal example of a system that undergoes a transition at a quantum critical point (QCP). The columbite CoNb2O6 is the closest realization of the transverse Ising magnet found to date. At low temperatures, neutron diffraction has observed a set of discrete collective spin modes near the QCP. Here, we ask if there are low-lying spin excitations distinct from these relatively high-energy modes. Using the heat capacity, we show that a significant band of gapless spin excitations exists. At the QCP, their spin entropy rises to a prominent peak that accounts for 30% of the total spin degrees of freedom. In a narrow field interval below the QCP, the gapless excitations display a fermion-like, temperature-linear heat capacity below 1 K. These novel gapless modes are the main spin excitations participating in, and affected by, the quantum transition. PMID:26146018

The quantum Ising chain with a generalized defect

NASA Astrophysics Data System (ADS)

Grimm, Uwe

1990-08-01

The finite-size scaling properties of the quantum Ising chain with different types of generalized defects are studied. This not only means an alteration of the coupling constant as previously examined, but also an additional arbitrary transformation in the algebra of observables at one site of the chain. One can distinguish between two classes of generalized defects: on the one hand those which do not affect the finite-size integrability of the Ising chain, and on the other hand those that destroy this property. In this context, finite-size integrability is always understood as a synonym for the possibility to write the hamiltonian of the finite chain as a bilinear expression in fermionic operators by means of a Jordan-Wigner transformation. Concerning the first type of defect, an exact solution for the scaling spectrum is obtained for the most universal defect that preserves the global Z2 symmetry of the chain. It is shown that in the continuum limit this yields the same result as for one properly chosen ordinary defect, that is changing the coupling constant only, and thus the finite-size scaling spectra can be described by irreps of a shifted u(1) Kac-Moody algebra. The other type of defect is examined by means of numerical finite-size calculations. In contrast to the first case, these calculations suggest a non-continuous dependence of the scaling dimensions on the defect parameters. A conjecture for the operator content involving only one primary field of a Virasoro algebra with central charge c= {1}/{2} is given.

Applications of ISES for meteorology

NASA Technical Reports Server (NTRS)

Try, Paul D.

1990-01-01

The results are summarized from an initial assessment of the potential real-time meteorological requirements for the data from Eos systems. Eos research scientists associated with facility instruments, investigator instruments, and interdisciplinary groups with data related to meteorological support were contacted, along with those from the normal operational user and technique development groups. Two types of activities indicated the greatest need for real-time Eos data: technology transfer groups (e.g., NOAA's Forecasting System Laboratory and the DOD development laboratories), and field testing groups with airborne operations. A special concern was expressed by several non-U.S. participants who desire a direct downlink to be sure of rapid receipt of the data for their area of interest. Several potential experiments or demonstrations are recommended for ISES which include support for hurricane/typhoon forecasting, space shuttle reentry, severe weather forecasting (using microphysical cloud classification techniques), field testing, and quick reaction of instrumented aircraft to measure such events as polar stratospheric clouds and volcanic eruptions.

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.

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

NREL and Fraunhofer ISE to Collaborate on Hydrogen and Fuel Cell Research |

Science.gov Websites

(R&D) activities to accelerate progress in these fields. NREL's long-term research and accelerate progress toward shared R&D goals and to ensure sustainable use of hydrogen and fuel cell Fraunhofer ISE in the following areas: Electrolysis, including cell, stack, and system R&D and

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.

Spacecraft potential control on ISEE-1

NASA Technical Reports Server (NTRS)

Gonfalone, A.; Pedersen, A.; Fahleson, U. V.; Faelthammar, C. G.; Mozer, F. S.; Torbert, R. B.

1979-01-01

Active control of the potential of the ISEE-1 satellite by the use of electron guns is reviewed. The electron guns contain a special cathode capable of emitting an electron current selectable between 10 to the -8th power and 10 to the -3rd power at energies from approximately .6 to 41 eV. Results obtained during flight show that the satellite potential can be stabilized at a value more positive than the normally positive floating potential. The electron guns also reduce the spin modulation of the spacecraft potential which is due to the aspect dependent photoemission of the long booms. Plasma parameters like electron temperature and density can be deduced from the variation of the spacecraft potential as a function of the gun current. The effects of electron beam emission on other experiments are briefly mentioned.

Hypergeometric Forms for Ising-Class Integrals

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

Bailey, David H.; Borwein, David; Borwein, Jonathan M.

2006-07-01

We apply experimental-mathematical principles to analyzecertain integrals relevant to the Ising theory of solid-state physics. Wefind representations of the these integrals in terms of MeijerG-functions and nested-Barnes integrals. Our investigations began bycomputing 500-digit numerical values of Cn,k,namely a 2-D array of Isingintegrals for all integers n, k where n is in [2,12]and k is in [0,25].We found that some Cn,k enjoy exact evaluations involving DirichletL-functions or the Riemann zeta function. In theprocess of analyzinghypergeometric representations, we found -- experimentally and strikingly-- that the Cn,k almost certainly satisfy certain inter-indicialrelations including discrete k-recursions. Using generating functions,differential theory, complex analysis, and Wilf-Zeilbergermore » algorithms weare able to prove some central cases of these relations.« less

Model-based Clustering of High-Dimensional Data in Astrophysics

NASA Astrophysics Data System (ADS)

Bouveyron, C.

2016-05-01

The nature of data in Astrophysics has changed, as in other scientific fields, in the past decades due to the increase of the measurement capabilities. As a consequence, data are nowadays frequently of high dimensionality and available in mass or stream. Model-based techniques for clustering are popular tools which are renowned for their probabilistic foundations and their flexibility. However, classical model-based techniques show a disappointing behavior in high-dimensional spaces which is mainly due to their dramatical over-parametrization. The recent developments in model-based classification overcome these drawbacks and allow to efficiently classify high-dimensional data, even in the "small n / large p" situation. This work presents a comprehensive review of these recent approaches, including regularization-based techniques, parsimonious modeling, subspace classification methods and classification methods based on variable selection. The use of these model-based methods is also illustrated on real-world classification problems in Astrophysics using R packages.

Magnetic ground state of the Ising-like antiferromagnet DyScO 3

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

Wu, L. S.; Nikitin, Stanislav E.; Frontzek, Matthias D.

2017-10-05

Here, we report on the low-temperature magnetic properties of the DyScO3 perovskite, which were characterized by means of single crystal and powder neutron scattering, and by magnetization measurements. Below T N = 3.15 K, Dy 3+ moments form an antiferromagnetic structure with an easy axis of magnetization lying in the ab plane. The magnetic moments are inclined at an angle of ~ ±28° to the b axis. We show that the ground-state Kramers doublet of Dy 3+ is made up of primarily |±15/2> eigenvectors and well separated by a crystal field from the first excited state at E 1 =more » 24.9 meV. This leads to an extreme Ising single-ion anisotropy, M ⊥/M ∥~0.05. The transverse magnetic fluctuations, which are proportional to M 2 ⊥/M 2 ∥, are suppressed, and only moment fluctuations along the local Ising direction are allowed. We also found that the Dy-Dy dipolar interactions along the crystallographic c axis are two to four times larger than in-plane interactions.« less

Complex-network description of thermal quantum states in the Ising spin chain

NASA Astrophysics Data System (ADS)

Sundar, Bhuvanesh; Valdez, Marc Andrew; Carr, Lincoln D.; Hazzard, Kaden R. A.

2018-05-01

We use network analysis to describe and characterize an archetypal quantum system—an Ising spin chain in a transverse magnetic field. We analyze weighted networks for this quantum system, with link weights given by various measures of spin-spin correlations such as the von Neumann and Rényi mutual information, concurrence, and negativity. We analytically calculate the spin-spin correlations in the system at an arbitrary temperature by mapping the Ising spin chain to fermions, as well as numerically calculate the correlations in the ground state using matrix product state methods, and then analyze the resulting networks using a variety of network measures. We demonstrate that the network measures show some traits of complex networks already in this spin chain, arguably the simplest quantum many-body system. The network measures give insight into the phase diagram not easily captured by more typical quantities, such as the order parameter or correlation length. For example, the network structure varies with transverse field and temperature, and the structure in the quantum critical fan is different from the ordered and disordered phases.

Coherent Ising machines—optical neural networks operating at the quantum limit

NASA Astrophysics Data System (ADS)

Yamamoto, Yoshihisa; Aihara, Kazuyuki; Leleu, Timothee; Kawarabayashi, Ken-ichi; Kako, Satoshi; Fejer, Martin; Inoue, Kyo; Takesue, Hiroki

2017-12-01

In this article, we will introduce the basic concept and the quantum feature of a novel computing system, coherent Ising machines, and describe their theoretical and experimental performance. We start with the discussion how to construct such physical devices as the quantum analog of classical neuron and synapse, and end with the performance comparison against various classical neural networks implemented in CPU and supercomputers.

Phase diagram and re-entrant fermionic entanglement in a hybrid Ising-Hubbard ladder

NASA Astrophysics Data System (ADS)

Sousa, H. S.; Pereira, M. S. S.; de Oliveira, I. N.; Strečka, J.; Lyra, M. L.

2018-05-01

The degree of fermionic entanglement is examined in an exactly solvable Ising-Hubbard ladder, which involves interacting electrons on the ladder's rungs described by Hubbard dimers at half-filling on each rung, accounting for intrarung hopping and Coulomb terms. The coupling between neighboring Hubbard dimers is assumed to have an Ising-like nature. The ground-state phase diagram consists of four distinct regions corresponding to the saturated paramagnetic, the classical antiferromagnetic, the quantum antiferromagnetic, and the mixed classical-quantum phase. We have exactly computed the fermionic concurrence, which measures the degree of quantum entanglement between the pair of electrons on the ladder rungs. The effects of the hopping amplitude, the Coulomb term, temperature, and magnetic fields on the fermionic entanglement are explored in detail. It is shown that the fermionic concurrence displays a re-entrant behavior when quantum entanglement is being generated at moderate temperatures above the classical saturated paramagnetic ground state.

Thermodynamic behavior and enhanced magnetocaloric effect in a frustrated spin-1/2 Ising-Heisenberg triangular tube

NASA Astrophysics Data System (ADS)

Alécio, Raphael Cavalcante; Strečka, Jozef; Lyra, Marcelo L.

2018-04-01

The thermodynamic behavior of an Ising-Heisenberg triangular tube with Heisenberg intra-rung and Ising inter-rung interactions is exactly obtained in an external magnetic field within the framework of the transfer-matrix method. We report rigorous results for the temperature dependence of the magnetization, entropy, pair correlations and specific heat, as well as typical iso-entropic curves. The discontinuous field-driven ground-state phase transitions are reflected in some anomalous thermodynamic behavior as for instance a striking low-temperature peak of the specific heat and an enhanced magnetocaloric effect. It is demonstrated that the intermediate magnetization plateaus shrink in and the relevant sharp edges associated with the magnetization jump round off upon increasing temperature.

THREE-DIMENSIONAL MODEL FOR HYPERTHERMIA CALCULATIONS

EPA Science Inventory

Realistic three-dimensional models that predict temperature distributions with a high degree of spatial resolution in bodies exposed to electromagnetic (EM) fields are required in the application of hyperthermia for cancer treatment. To ascertain the thermophysiologic response of...

VALIDITY OF A TWO-DIMENSIONAL MODEL FOR VARIABLE-DENSITY HYDRODYNAMIC CIRCULATION

EPA Science Inventory

A three-dimensional model of temperatures and currents has been formulated to assist in the analysis and interpretation of the dynamics of stratified lakes. In this model, nonlinear eddy coefficients for viscosity and conductivities are included. A two-dimensional model (one vert...

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.

Three-dimensional finite element modelling of muscle forces during mastication.

PubMed

Röhrle, Oliver; Pullan, Andrew J

2007-01-01

This paper presents a three-dimensional finite element model of human mastication. Specifically, an anatomically realistic model of the masseter muscles and associated bones is used to investigate the dynamics of chewing. A motion capture system is used to track the jaw motion of a subject chewing standard foods. The three-dimensional nonlinear deformation of the masseter muscles are calculated via the finite element method, using the jaw motion data as boundary conditions. Motion-driven muscle activation patterns and a transversely isotropic material law, defined in a muscle-fibre coordinate system, are used in the calculations. Time-force relationships are presented and analysed with respect to different tasks during mastication, e.g. opening, closing, and biting, and are also compared to a more traditional one-dimensional model. The results strongly suggest that, due to the complex arrangement of muscle force directions, modelling skeletal muscles as conventional one-dimensional lines of action might introduce a significant source of error.

Particle orbits in two-dimensional equilibrium models for the magnetotail

NASA Technical Reports Server (NTRS)

Karimabadi, H.; Pritchett, P. L.; Coroniti, F. V.

1990-01-01

Assuming that there exist an equilibrium state for the magnetotail, particle orbits are investigated in two-dimensional kinetic equilibrium models for the magnetotail. Particle orbits in the equilibrium field are compared with those calculated earlier with one-dimensional models, where the main component of the magnetic field (Bx) was approximated as either a hyperbolic tangent or a linear function of z with the normal field (Bz) assumed to be a constant. It was found that the particle orbits calculated with the two types of models are significantly different, mainly due to the neglect of the variation of Bx with x in the one-dimensional fields.

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.

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.

Adaptive multi-GPU Exchange Monte Carlo for the 3D Random Field Ising Model

NASA Astrophysics Data System (ADS)

Navarro, Cristóbal A.; Huang, Wei; Deng, Youjin

2016-08-01

This work presents an adaptive multi-GPU Exchange Monte Carlo approach for the simulation of the 3D Random Field Ising Model (RFIM). The design is based on a two-level parallelization. The first level, spin-level parallelism, maps the parallel computation as optimal 3D thread-blocks that simulate blocks of spins in shared memory with minimal halo surface, assuming a constant block volume. The second level, replica-level parallelism, uses multi-GPU computation to handle the simulation of an ensemble of replicas. CUDA's concurrent kernel execution feature is used in order to fill the occupancy of each GPU with many replicas, providing a performance boost that is more notorious at the smallest values of L. In addition to the two-level parallel design, the work proposes an adaptive multi-GPU approach that dynamically builds a proper temperature set free of exchange bottlenecks. The strategy is based on mid-point insertions at the temperature gaps where the exchange rate is most compromised. The extra work generated by the insertions is balanced across the GPUs independently of where the mid-point insertions were performed. Performance results show that spin-level performance is approximately two orders of magnitude faster than a single-core CPU version and one order of magnitude faster than a parallel multi-core CPU version running on 16-cores. Multi-GPU performance is highly convenient under a weak scaling setting, reaching up to 99 % efficiency as long as the number of GPUs and L increase together. The combination of the adaptive approach with the parallel multi-GPU design has extended our possibilities of simulation to sizes of L = 32 , 64 for a workstation with two GPUs. Sizes beyond L = 64 can eventually be studied using larger multi-GPU systems.

Analysis of the Three-Dimensional Vector FAÇADE Model Created from Photogrammetric Data

NASA Astrophysics Data System (ADS)

Kamnev, I. S.; Seredovich, V. A.

2017-12-01

The results of the accuracy assessment analysis for creation of a three-dimensional vector model of building façade are described. In the framework of the analysis, analytical comparison of three-dimensional vector façade models created by photogrammetric and terrestrial laser scanning data has been done. The three-dimensional model built from TLS point clouds was taken as the reference one. In the course of the experiment, the three-dimensional model to be analyzed was superimposed on the reference one, the coordinates were measured and deviations between the same model points were determined. The accuracy estimation of the three-dimensional model obtained by using non-metric digital camera images was carried out. Identified façade surface areas with the maximum deviations were revealed.

One-Dimensional Harmonic Model for Biomolecules

PubMed Central

Krizan, John E.

1973-01-01

Following in spirit a paper by Rosen, we propose a one-dimensional harmonic model for biomolecules. Energy bands with gaps of the order of semi-conductor gaps are found. The method is discussed for general symmetric and periodic potential functions. PMID:4709518

Comparative analysis for strength serum sodium and potassium in three different methods: Flame photometry, ion-selective electrode (ISE) and colorimetric enzymatic.

PubMed

Garcia, Rafaela Alvim; Vanelli, Chislene Pereira; Pereira Junior, Olavo Dos Santos; Corrêa, José Otávio do Amaral

2018-06-19

Hydroelectrolytic disorders are common in clinical situations and may be harmful to the patient, especially those involving plasma sodium and potassium dosages. Among the possible methods for the dosages are flame photometry, ion-selective electrode (ISE) and colorimetric enzymatic method. We analyzed 175 samples in the three different methods cited from patients attending the laboratory of the University Hospital of the Federal University of Juiz de Fora. The values obtained were statistically treated using SPSS 19.0 software. The present study aims to evaluate the impact of the use of these different methods in the determination of plasma sodium and potassium. The averages obtained for sodium and potassium measurements by flame photometry were similar (P > .05) to the means obtained for the two electrolytes by ISE. The averages obtained by the colorimetric enzymatic method presented statistical difference in relation to ISE, both for sodium and potassium. In the correlation analysis, both flame photometry and colorimetric enzymatic showed a strong correlation with the ISE method for both dosages. At the first time in the same work sodium and potassium were analyzed by three different methods and the results allowed us to conclude that the methods showed a positive and strong correlation, and can be applied in the clinical routine. © 2018 Wiley Periodicals, Inc.

Exact solution of three-dimensional transport problems using one-dimensional models. [in semiconductor devices

NASA Technical Reports Server (NTRS)

Misiakos, K.; Lindholm, F. A.

1986-01-01

Several parameters of certain three-dimensional semiconductor devices including diodes, transistors, and solar cells can be determined without solving the actual boundary-value problem. The recombination current, transit time, and open-circuit voltage of planar diodes are emphasized here. The resulting analytical expressions enable determination of the surface recombination velocity of shallow planar diodes. The method involves introducing corresponding one-dimensional models having the same values of these parameters.

An Energy Model of Place Cell Network in Three Dimensional Space.

PubMed

Wang, Yihong; Xu, Xuying; Wang, Rubin

2018-01-01

Place cells are important elements in the spatial representation system of the brain. A considerable amount of experimental data and classical models are achieved in this area. However, an important question has not been addressed, which is how the three dimensional space is represented by the place cells. This question is preliminarily surveyed by energy coding method in this research. Energy coding method argues that neural information can be expressed by neural energy and it is convenient to model and compute for neural systems due to the global and linearly addable properties of neural energy. Nevertheless, the models of functional neural networks based on energy coding method have not been established. In this work, we construct a place cell network model to represent three dimensional space on an energy level. Then we define the place field and place field center and test the locating performance in three dimensional space. The results imply that the model successfully simulates the basic properties of place cells. The individual place cell obtains unique spatial selectivity. The place fields in three dimensional space vary in size and energy consumption. Furthermore, the locating error is limited to a certain level and the simulated place field agrees to the experimental results. In conclusion, this is an effective model to represent three dimensional space by energy method. The research verifies the energy efficiency principle of the brain during the neural coding for three dimensional spatial information. It is the first step to complete the three dimensional spatial representing system of the brain, and helps us further understand how the energy efficiency principle directs the locating, navigating, and path planning function of the brain.

Electronic transport on the Shastry-Sutherland lattice in Ising-type rare-earth tetraborides

NASA Astrophysics Data System (ADS)

Ye, Linda; Suzuki, Takehito; Checkelsky, Joseph G.

2017-05-01

In the presence of a magnetic field frustrated spin systems may exhibit plateaus at fractional values of saturation magnetization. Such plateau states are stabilized by classical and quantum mechanisms including order by disorder, triplon crystallization, and various competing order effects. In the case of electrically conducting systems, free electrons represent an incisive probe for the plateau states. Here we study the electrical transport of Ising-type rare-earth tetraborides R B4 (R =Er , Tm), a metallic Shastry-Sutherland lattice showing magnetization plateaus. We find that the longitudinal and transverse resistivities reflect scattering with both the static and the dynamic plateau structure. We model these results consistently with the expected strong uniaxial anisotropy on a quantitative level, providing a framework for the study of plateau states in metallic frustrated systems.

Detection of Subtle Context-Dependent Model Inaccuracies in High-Dimensional Robot Domains.

PubMed

Mendoza, Juan Pablo; Simmons, Reid; Veloso, Manuela

2016-12-01

Autonomous robots often rely on models of their sensing and actions for intelligent decision making. However, when operating in unconstrained environments, the complexity of the world makes it infeasible to create models that are accurate in every situation. This article addresses the problem of using potentially large and high-dimensional sets of robot execution data to detect situations in which a robot model is inaccurate-that is, detecting context-dependent model inaccuracies in a high-dimensional context space. To find inaccuracies tractably, the robot conducts an informed search through low-dimensional projections of execution data to find parametric Regions of Inaccurate Modeling (RIMs). Empirical evidence from two robot domains shows that this approach significantly enhances the detection power of existing RIM-detection algorithms in high-dimensional spaces.

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.

Supersymmetric gauged matrix models from dimensional reduction on a sphere

NASA Astrophysics Data System (ADS)

Closset, Cyril; Ghim, Dongwook; Seong, Rak-Kyeong

2018-05-01

It was recently proposed that N = 1 supersymmetric gauged matrix models have a duality of order four — that is, a quadrality — reminiscent of infrared dualities of SQCD theories in higher dimensions. In this note, we show that the zero-dimensional quadrality proposal can be inferred from the two-dimensional Gadde-Gukov-Putrov triality. We consider two-dimensional N = (0, 2) SQCD compactified on a sphere with the half-topological twist. For a convenient choice of R-charge, the zero-mode sector on the sphere gives rise to a simple N = 1 gauged matrix model. Triality on the sphere then implies a triality relation for the supersymmetric matrix model, which can be completed to the full quadrality.

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.

Multiexponential models of (1+1)-dimensional dilaton gravity and Toda-Liouville integrable models

NASA Astrophysics Data System (ADS)

de Alfaro, V.; Filippov, A. T.

2010-01-01

We study general properties of a class of two-dimensional dilaton gravity (DG) theories with potentials containing several exponential terms. We isolate and thoroughly study a subclass of such theories in which the equations of motion reduce to Toda and Liouville equations. We show that the equation parameters must satisfy a certain constraint, which we find and solve for the most general multiexponential model. It follows from the constraint that integrable Toda equations in DG theories generally cannot appear without accompanying Liouville equations. The most difficult problem in the two-dimensional Toda-Liouville (TL) DG is to solve the energy and momentum constraints. We discuss this problem using the simplest examples and identify the main obstacles to solving it analytically. We then consider a subclass of integrable two-dimensional theories where scalar matter fields satisfy the Toda equations and the two-dimensional metric is trivial. We consider the simplest case in some detail. In this example, we show how to obtain the general solution. We also show how to simply derive wavelike solutions of general TL systems. In the DG theory, these solutions describe nonlinear waves coupled to gravity and also static states and cosmologies. For static states and cosmologies, we propose and study a more general one-dimensional TL model typically emerging in one-dimensional reductions of higher-dimensional gravity and supergravity theories. We especially attend to making the analytic structure of the solutions of the Toda equations as simple and transparent as possible.

Computational technique and performance of Transient Inundation Model for Rivers--2 Dimensional (TRIM2RD) : a depth-averaged two-dimensional flow model

USGS Publications Warehouse

Fulford, Janice M.

2003-01-01

A numerical computer model, Transient Inundation Model for Rivers -- 2 Dimensional (TrimR2D), that solves the two-dimensional depth-averaged flow equations is documented and discussed. The model uses a semi-implicit, semi-Lagrangian finite-difference method. It is a variant of the Trim model and has been used successfully in estuarine environments such as San Francisco Bay. The abilities of the model are documented for three scenarios: uniform depth flows, laboratory dam-break flows, and large-scale riverine flows. The model can start computations from a ?dry? bed and converge to accurate solutions. Inflows are expressed as source terms, which limits the use of the model to sufficiently long reaches where the flow reaches equilibrium with the channel. The data sets used by the investigation demonstrate that the model accurately propagates flood waves through long river reaches and simulates dam breaks with abrupt water-surface changes.

Instrument for Solvent Extraction and Analysis (ISEE) of Organics from Regolith Simulant Using Supercritical Fluid Extraction and Chromatography

NASA Technical Reports Server (NTRS)

Franco, Carolina; Hintze, Paul E.

2017-01-01

ISEE is an instrument with the potential to perform extractions from regolith found on the surface of asteroids and planets, followed by characterization and quantitation of the extracts using supercritical fluid extraction (SFE) and chromatography (SFC). SFE is a developed technique proven to extract a wide range of organic compounds. SFC is similar to High Performance Liquid Chromatography (HPLC) but has the advantage of performing chiral separations without needing to derivatize the chiral compounds. CO2 will be the solvent for both stages as it is readily available in the Mars atmosphere. ISEE will capture CO2 from the environment, and use it for SFE and SFC. If successful, this would allow ISEE to perform analysis of organic compounds without using consumables. This paper will present results on a preliminary, proof-of-principle effort to use SFE and SFC to extract and analyze lunar regolith simulant spiked with organic compounds representing a range of organics that ISEE would expect to characterize. An optimization of variables for the extraction of the organics from the spiked regolith was successfully developed, using 138 bar pressure and 40 C temperature. The extraction flow rate was optimized at 2% SLPM with 30% methanol modifier. The extractions were successful with a value of 77.3+/- 0.9% of organics extracted. However, the recovery of organics after the extraction was very low with only 48.5+/-14.2%. Moreover, three columns were selected to analyze multiple samples at a time; two of them are Viridis HSS C18 SB and Torus DIOL, and the third column, specific for chiral separations, has not yet been selected yet.

Fractional calculus phenomenology in two-dimensional plasma models

NASA Astrophysics Data System (ADS)

Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill

2006-10-01

Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).

Conical pitch angle distributions of very low-energy ion fluxes observed by ISEE 1

NASA Technical Reports Server (NTRS)

Horwitz, J. L.; Baugher, C. R.; Chappell, C. R.; Shelley, E. G.; Young, D. T.

1982-01-01

Observations are presented of conical distributions of low-energy ion fluxes from throughout the magnetosphere. The data were provided by the plasma composition experiment (PCE) on ISEE 1. ISEE 1 was launched in October 1977 into a highly elliptical orbit with a 30 deg inclination to the equator and 22.5 earth radii apogee. Particular attention is given to data taken when the instrument was in its thermal plasma mode, sampling ions in the energy per charge range 0-100 eV/e. Attention is given to examples of conical distributions in 0- to 100-eV/e ions, the occurrence of conical distributions of 0- to 100-eV ions in local time-geocentric distance and latitude-geocentric distance coordinates, the cone angles in 0- to 100-eV ion conics, Kp distributions of 0- to 100-eV ion conics, and some compositional aspects of 0- to 100-eV ion conics.

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).

Three-dimensional cell culture models for investigating human viruses.

PubMed

He, Bing; Chen, Guomin; Zeng, Yi

2016-10-01

Three-dimensional (3D) culture models are physiologically relevant, as they provide reproducible results, experimental flexibility and can be adapted for high-throughput experiments. Moreover, these models bridge the gap between traditional two-dimensional (2D) monolayer cultures and animal models. 3D culture systems have significantly advanced basic cell science and tissue engineering, especially in the fields of cell biology and physiology, stem cell research, regenerative medicine, cancer research, drug discovery, and gene and protein expression studies. In addition, 3D models can provide unique insight into bacteriology, virology, parasitology and host-pathogen interactions. This review summarizes and analyzes recent progress in human virological research with 3D cell culture models. We discuss viral growth, replication, proliferation, infection, virus-host interactions and antiviral drugs in 3D culture models.

Modelling Parsing Constraints with High-Dimensional Context Space.