One-Dimensional Ising Model with "k"-Spin Interactions
ERIC Educational Resources Information Center
Fan, Yale
2011-01-01
We examine a generalization of the one-dimensional Ising model involving interactions among neighbourhoods of "k" adjacent spins. The model is solved by exploiting a connection to an interesting computational problem that we call ""k"-SAT on a ring", and is shown to be equivalent to the nearest-neighbour Ising model in the absence of an external…
Bootstrapping Critical Ising Model on Three Dimensional Real Projective Space.
Nakayama, Yu
2016-04-01
Given conformal data on a flat Euclidean space, we use crosscap conformal bootstrap equations to numerically solve the Lee-Yang model as well as the critical Ising model on a three dimensional real projective space. We check the rapid convergence of our bootstrap program in two dimensions from the exact solutions available. Based on the comparison, we estimate that our systematic error on the numerically solved one-point functions of the critical Ising model on a three dimensional real projective space is less than 1%. Our method opens up a novel way to solve conformal field theories on nontrivial geometries. PMID:27104697
Bootstrapping Critical Ising Model on Three Dimensional Real Projective Space
NASA Astrophysics Data System (ADS)
Nakayama, Yu
2016-04-01
Given conformal data on a flat Euclidean space, we use crosscap conformal bootstrap equations to numerically solve the Lee-Yang model as well as the critical Ising model on a three dimensional real projective space. We check the rapid convergence of our bootstrap program in two dimensions from the exact solutions available. Based on the comparison, we estimate that our systematic error on the numerically solved one-point functions of the critical Ising model on a three dimensional real projective space is less than 1%. Our method opens up a novel way to solve conformal field theories on nontrivial geometries.
One-dimensional Ising model with multispin interactions
NASA Astrophysics Data System (ADS)
Turban, Loïc
2016-09-01
We study the spin-1/2 Ising chain with multispin interactions K involving the product of m successive spins, for general values of m. Using a change of spin variables the zero-field partition function of a finite chain is obtained for free and periodic boundary conditions and we calculate the two-spin correlation function. When placed in an external field H the system is shown to be self-dual. Using another change of spin variables the one-dimensional Ising model with multispin interactions in a field is mapped onto a zero-field rectangular Ising model with first-neighbour interactions K and H. The 2D system, with size m × N/m, has the topology of a cylinder with helical BC. In the thermodynamic limit N/m\\to ∞ , m\\to ∞ , a 2D critical singularity develops on the self-duality line, \\sinh 2K\\sinh 2H=1.
Thermodynamics of trajectories of the one-dimensional Ising model
NASA Astrophysics Data System (ADS)
Loscar, Ernesto S.; Mey, Antonia S. J. S.; Garrahan, Juan P.
2011-12-01
We present a numerical study of the dynamics of the one-dimensional Ising model by applying the large-deviation method to describe ensembles of dynamical trajectories. In this approach trajectories are classified according to a dynamical order parameter and the structure of ensembles of trajectories can be understood from the properties of large-deviation functions, which play the role of dynamical free-energies. We consider both Glauber and Kawasaki dynamics, and also the presence of a magnetic field. For Glauber dynamics in the absence of a field we confirm the analytic predictions of Jack and Sollich about the existence of critical dynamical, or space-time, phase transitions at critical values of the 'counting' field s. In the presence of a magnetic field the dynamical phase diagram also displays first order transition surfaces. We discuss how these non-equilibrium transitions in the 1d Ising model relate to the equilibrium ones of the 2d Ising model. For Kawasaki dynamics we find a much simpler dynamical phase structure, with transitions reminiscent of those seen in kinetically constrained models.
Information theoretic aspects of the two-dimensional Ising model.
Lau, Hon Wai; Grassberger, Peter
2013-02-01
We present numerical results for various information theoretic properties of the square lattice Ising model. First, using a bond propagation algorithm, we find the difference 2H(L)(w)-H(2L)(w) between entropies on cylinders of finite lengths L and 2L with open end cap boundaries, in the limit L→∞. This essentially quantifies how the finite length correction for the entropy scales with the cylinder circumference w. Secondly, using the transfer matrix, we obtain precise estimates for the information needed to specify the spin state on a ring encircling an infinitely long cylinder. Combining both results, we obtain the mutual information between the two halves of a cylinder (the "excess entropy" for the cylinder), where we confirm with higher precision but for smaller systems the results recently obtained by Wilms et al., and we show that the mutual information between the two halves of the ring diverges at the critical point logarithmically with w. Finally, we use the second result together with Monte Carlo simulations to show that also the excess entropy of a straight line of n spins in an infinite lattice diverges at criticality logarithmically with n. We conjecture that such logarithmic divergence happens generically for any one-dimensional subset of sites at any two-dimensional second-order phase transition. Comparing straight lines on square and triangular lattices with square loops and with lines of thickness 2, we discuss questions of universality. PMID:23496480
Information theoretic aspects of the two-dimensional Ising model
NASA Astrophysics Data System (ADS)
Lau, Hon Wai; Grassberger, Peter
2013-02-01
We present numerical results for various information theoretic properties of the square lattice Ising model. First, using a bond propagation algorithm, we find the difference 2HL(w)-H2L(w) between entropies on cylinders of finite lengths L and 2L with open end cap boundaries, in the limit L→∞. This essentially quantifies how the finite length correction for the entropy scales with the cylinder circumference w. Secondly, using the transfer matrix, we obtain precise estimates for the information needed to specify the spin state on a ring encircling an infinitely long cylinder. Combining both results, we obtain the mutual information between the two halves of a cylinder (the “excess entropy” for the cylinder), where we confirm with higher precision but for smaller systems the results recently obtained by Wilms , and we show that the mutual information between the two halves of the ring diverges at the critical point logarithmically with w. Finally, we use the second result together with Monte Carlo simulations to show that also the excess entropy of a straight line of n spins in an infinite lattice diverges at criticality logarithmically with n. We conjecture that such logarithmic divergence happens generically for any one-dimensional subset of sites at any two-dimensional second-order phase transition. Comparing straight lines on square and triangular lattices with square loops and with lines of thickness 2, we discuss questions of universality.
Algorithmic proof for the completeness of the two-dimensional Ising model
NASA Astrophysics Data System (ADS)
Karimipour, Vahid; Zarei, Mohammad Hossein
2012-11-01
We show that the two-dimensional (2D) Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all its spin-spin coupling equal to i(π)/(4) and all parameters of the original model are contained in the local magnetic fields of the Ising model. This result has already been derived by using techniques from quantum information theory and by exploiting the universality of cluster states. Here we do not use the quantum formalism and hence make the completeness result accessible to a wide audience. Furthermore, our method has the advantage of being algorithmic in nature so that, by following a set of simple graphical transformations, one is able to transform any discrete lattice model to an Ising model defined on a (polynomially) larger 2D lattice.
Mathematical structure of the three-dimensional (3D) Ising model
NASA Astrophysics Data System (ADS)
Zhang, Zhi-Dong
2013-03-01
An overview of the mathematical structure of the three-dimensional (3D) Ising model is given from the points of view of topology, algebra, and geometry. By analyzing the relationships among transfer matrices of the 3D Ising model, Reidemeister moves in the knot theory, Yang-Baxter and tetrahedron equations, the following facts are illustrated for the 3D Ising model. 1) The complex quaternion basis constructed for the 3D Ising model naturally represents the rotation in a (3+1)-dimensional space-time as a relativistic quantum statistical mechanics model, which is consistent with the 4-fold integrand of the partition function obtained by taking the time average. 2) A unitary transformation with a matrix that is a spin representation in 2n·l·o-space corresponds to a rotation in 2n·l·o-space, which serves to smooth all the crossings in the transfer matrices and contributes the non-trivial topological part of the partition function of the 3D Ising model. 3) A tetrahedron relationship would ensure the commutativity of the transfer matrices and the integrability of the 3D Ising model, and its existence is guaranteed by the Jordan algebra and the Jordan-von Neumann-Wigner procedures. 4) The unitary transformation for smoothing the crossings in the transfer matrices changes the wave functions by complex phases varphix, varphiy, and varphiz. The relationship with quantum field and gauge theories and the physical significance of the weight factors are discussed in detail. The conjectured exact solution is compared with numerical results, and the singularities at/near infinite temperature are inspected. The analyticity in β = 1/(kBT) of both the hard-core and the Ising models has been proved only for β > 0, not for β = 0. Thus the high-temperature series cannot serve as a standard for judging a putative exact solution of the 3D Ising model.
Linear relaxation in large two-dimensional Ising models
NASA Astrophysics Data System (ADS)
Lin, Y.; Wang, F.
2016-02-01
Critical dynamics in two-dimension Ising lattices up to 2048 ×2048 is simulated on field-programmable-gate-array- based computing devices. Linear relaxation times are measured from extremely long Monte Carlo simulations. The longest simulation has 7.1 ×1016 spin updates, which would take over 37 years to simulate on a general purpose computer. The linear relaxation time of the Ising lattices is found to follow the dynamic scaling law for correlation lengths as long as 2048. The dynamic exponent z of the system is found to be 2.179(12), which is consistent with previous studies of Ising lattices with shorter correlation lengths. It is also found that Monte Carlo simulations of critical dynamics in Ising lattices larger than 512 ×512 are very sensitive to the statistical correlations between pseudorandom numbers, making it even more difficult to study such large systems.
One-dimensional random field Ising model and discrete stochastic mappings
Behn, U.; Zagrebnov, V.A.
1987-06-01
Previous results relating the one-dimensional random field Ising model to a discrete stochastic mapping are generalized to a two-valued correlated random (Markovian) field and to the case of zero temperature. The fractal dimension of the support of the invariant measure is calculated in a simple approximation and its dependence on the physical parameters is discussed.
Phase diagram of the three-dimensional axial next-nearest-neighbor Ising model
NASA Astrophysics Data System (ADS)
Gendiar, A.; Nishino, T.
2005-01-01
The three-dimensional axial next-nearest-neighbor Ising model is studied by a modified tensor product variational approach. A global phase diagram is constructed with numerous commensurate and incommensurate magnetic phases. The devil’s stairs behavior for the model is confirmed. The wavelength of the spin modulated phases increases to infinity at the boundary with the ferromagnetic phase. Widths of the commensurate phases are considerably narrower than those calculated by mean-field approximations.
NASA Astrophysics Data System (ADS)
Merdan, Ziya; Karakuş, Özlem
2016-07-01
The six dimensional Ising model with nearest-neighbor pair interactions has been simulated and verified numerically on the Creutz Cellular Automaton by using five bit demons near the infinite-lattice critical temperature with the linear dimensions L=4,6,8,10. The order parameter probability distribution for six dimensional Ising model has been calculated at the critical temperature. The constants of the analytical function have been estimated by fitting to probability function obtained numerically at the finite size critical point.
Statics and Dynamics of a Two-Dimensional Ising Spin-Glass Model
NASA Astrophysics Data System (ADS)
Young, A. P.
1983-03-01
The temperature and field dependence of spatial correlations and relaxation times are investigated in detail by Monte Carlo simulations for a two-dimensional Ising spin-glass model. There is no transition, but, in zero field, barrier heights and correlation range increase smoothly at low temperatures. This increase does not seem to be fast enough to explain experiments. In a field, barrier heights and the correlation length tend to a finite limit as T-->0. Points in the h-T plane with constant relaxation time satisfy T(h)-T(0)~h23 at moderately low temperatures.
Finite-size scaling and the three-dimensional Ising model
NASA Astrophysics Data System (ADS)
Bhanot, G.; Duke, D.; Salvador, R.
1986-06-01
We give results of an extensive finite-size-scaling analysis of the three-dimensional Ising model on lattices of size up to 443. Contrary to the results of Barber et al.
Two-dimensional XXZ -Ising model on a square-hexagon lattice
NASA Astrophysics Data System (ADS)
Valverde, J. S.; Rojas, Onofre; de Souza, S. M.
2009-04-01
We study a two-dimensional XXZ -Ising model on a square-hexagon (denoted for simplicity by 4-6) lattice with spin 1/2. The phase diagram at zero temperature is discussed, where five states are found, two types of ferrimagnetic states, two types of antiferromagnetic states, and one ferromagnetic state. To solve this model, we have mapped onto the eight-vertex model with union Jack interaction term, and it was verified that the model cannot be completely mapped onto eight-vertex model. However, by imposing an exact solution condition, we have found the region where the XXZ -Ising model on 4-6 lattice is exactly soluble with one free parameter, particularly for the case of symmetric eight-vertex model condition. In this manner we have explored the properties of the system and have analyzed the interacting competition parameters which preserve the region where there is an exact solution. Unfortunately the present model does not satisfy the free fermion condition of the eight-vertex model, unless for a trivial solution. Even so, we are able to discuss the critical point region, beyond the region of exact resolvability.
Flocking with discrete symmetry: The two-dimensional active Ising model
NASA Astrophysics Data System (ADS)
Solon, A. P.; Tailleur, J.
2015-10-01
We study in detail the active Ising model, a stochastic lattice gas where collective motion emerges from the spontaneous breaking of a discrete symmetry. On a two-dimensional lattice, active particles undergo a diffusion biased in one of two possible directions (left and right) and align ferromagnetically their direction of motion, hence yielding a minimal flocking model with discrete rotational symmetry. We show that the transition to collective motion amounts in this model to a bona fide liquid-gas phase transition in the canonical ensemble. The phase diagram in the density-velocity parameter plane has a critical point at zero velocity which belongs to the Ising universality class. In the density-temperature "canonical" ensemble, the usual critical point of the equilibrium liquid-gas transition is sent to infinite density because the different symmetries between liquid and gas phases preclude a supercritical region. We build a continuum theory which reproduces qualitatively the behavior of the microscopic model. In particular, we predict analytically the shapes of the phase diagrams in the vicinity of the critical points, the binodal and spinodal densities at coexistence, and the speeds and shapes of the phase-separated profiles.
Critical behavior of the two-dimensional Ising model with long-range correlated disorder
NASA Astrophysics Data System (ADS)
Dudka, M.; Fedorenko, A. A.; Blavatska, V.; Holovatch, Yu.
2016-06-01
We study critical behavior of the diluted two-dimensional Ising model in the presence of disorder correlations which decay algebraically with distance as ˜r-a . Mapping the problem onto two-dimensional Dirac fermions with correlated disorder we calculate the critical properties using renormalization group up to two-loop order. We show that beside the Gaussian fixed point the flow equations have a nontrivial fixed point which is stable for 0.995
Detect genuine multipartite entanglement in the one-dimensional transverse-field Ising model
Deng Dongling; Gu Shijian; Chen Jingling
2010-02-15
Recently Seevinck and Uffink argued that genuine multipartite entanglement (GME) had not been established in the experiments designed to confirm GME. In this paper, we use the Bell-type inequalities introduced by Seevinck and Svetlichny [M. Seevinck, G. Svetlichny, Phys. Rev. Lett. 89 (2002) 060401] to investigate the GME problem in the one-dimensional transverse-field Ising model. We show explicitly that the ground states of this model violate the inequality when the external transverse magnetic field is weak, which indicate that the ground states in this model with weak magnetic field are fully entangled. Since this model can be simulated with nuclear magnetic resonance, our results provide a fresh approach to experimental test of GME.
Liu, Y; Dilger, J P
1993-01-01
The Ising model of statistical physics provides a framework for studying systems of protomers in which nearest neighbors interact with each other. In this article, the Ising model is applied to the study of cooperative phenomena between ligand-gated ion channels. Expressions for the mean open channel probability, rho o, and the variance, sigma 2, are derived from the grand partition function. In the one-dimensional Ising model, interactions between neighboring open channels give rise to a sigmoidal rho o versus concentration curve and a nonquadratic relationship between sigma 2 and rho o. Positive cooperativity increases the slope at the midpoint of the rho o versus concentration curve, shifts the apparent binding affinity to lower concentrations, and increases the variance for a given rho o. Negative cooperativity has the opposite effects. Strong negative cooperativity results in a bimodal sigma 2 versus rho o curve. The slope of the rho o versus concentration curve increases linearly with the number of binding sites on a protomer, but the sigma 2 versus rho o relationship is independent of the number of ligand binding sites. Thus, the sigma 2 versus rho o curve provides unambiguous information about channel interactions. In the two-dimensional Ising model, rho o and sigma 2 are calculated numerically from a series expansion of the grand partition function appropriate for weak interactions. Virtually all of the features exhibited by the one-dimensional model are qualitatively present in the two-dimensional model. These models are also applicable to voltage-gated ion channels. PMID:7679298
Rényi entropy of a line in two-dimensional Ising models
NASA Astrophysics Data System (ADS)
Stéphan, J.-M.; Misguich, G.; Pasquier, V.
2010-09-01
We consider the two-dimensional Ising model on an infinitely long cylinder and study the probabilities pi to observe a given spin configuration i along a circular section of the cylinder. These probabilities also occur as eigenvalues of reduced density matrices in some Rokhsar-Kivelson wave functions. We analyze the subleading constant to the Rényi entropy Rn=1/(1-n)ln(∑ipin) and discuss its scaling properties at the critical point. Studying three different microscopic realizations, we provide numerical evidence that it is universal and behaves in a steplike fashion as a function of n with a discontinuity at the Shannon point n=1 . As a consequence, a field theoretical argument based on the replica trick would fail to give the correct value at this point. We nevertheless compute it numerically with high precision. Two other values of the Rényi parameter are of special interest: n=1/2 and n=∞ are related in a simple way to the Affleck-Ludwig boundary entropies associated to free and fixed boundary conditions, respectively.
Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models.
Labuhn, Henning; Barredo, Daniel; Ravets, Sylvain; de Léséleuc, Sylvain; Macrì, Tommaso; Lahaye, Thierry; Browaeys, Antoine
2016-06-30
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. PMID:27281203
Johnson, Jason K; Chertkov, Michael; Netrapalli, Praneeth
2010-11-12
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 our attention on the class of planar Ising models, for which inference is tractable using techniques of statistical physics [Kac and Ward; Kasteleyn]. Based on these techniques and recent methods for planarity testing and planar embedding [Chrobak and Payne], we propose a simple greedy algorithm for learning the best 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. We present the results of numerical experiments evaluating the performance of our algorithm.
NASA Astrophysics Data System (ADS)
Liu, Cheng-cheng; Shi, Jia-dong; Ding, Zhi-yong; Ye, Liu
2016-08-01
In this paper, the effect of external magnet field g on the relationship among the quantum discord, Bell non-locality and quantum phase transition by employing quantum renormalization-group (QRG) method in the one-dimensional transverse Ising model is investigated. In our model, external magnet field g can influence the phase diagrams. The results have shown that both the two quantum correlation measures can develop two saturated values, which are associated with two distinct phases: long-ranged ordered Ising phase and the paramagnetic phase with the number of QRG iterations increasing. Additionally, quantum non-locality always existent in the long-ranged ordered Ising phase no matter whatever the value of g is and what times QRG steps are carried out and we conclude that the quantum non-locality always exists not only suitable for the two sites of block, but for nearest-neighbor blocks in the long-ranged ordered Ising phase. However, the block-block correlation in the paramagnetic phase is not strong enough to violate the Bell-CHSH inequality as the size of system becomes large. Furthermore, when the system violates the CHSH inequality, i.e., satisfies quantum non-locality, it needs to be entangled. On the other way, if the system obeys the CHSH inequality, it may be entangled or not. To gain further insight, the non-analytic and scaling behavior of QD and Bell non-locality have also been analyzed in detail and this phenomenon indicates that the behavior of the correlation can perfectly help one to observe the quantum critical properties of the model.
NASA Astrophysics Data System (ADS)
Park, Sung-Been; Cha, Min-Chul
2015-11-01
We investigate the finite-size scaling properties of the quantum phase transition in the one-dimensional quantum Ising model with periodic boundary conditions by representing the ground state in matrix product state forms. The infinite time-evolving block decimation technique is used to optimize the states. A trace over a product of the matrices multiplied as many times as the number of sites yields the finite-size effects. For sufficiently large Schmidt ranks, the finite-size scaling behavior determines the critical point and the critical exponents whose values are consistent with the analytical results.
Topological Characterization of Extended Quantum Ising Models
NASA Astrophysics Data System (ADS)
Zhang, G.; Song, Z.
2015-10-01
We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic X Y model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the X Y model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is shown that the variation of the ground state energy density, which is a function of the loop, experiences a nonanalytical point when the winding number of the corresponding loop changes. The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model, which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram.
Topological Characterization of Extended Quantum Ising Models.
Zhang, G; Song, Z
2015-10-23
We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic XY model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the XY model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is shown that the variation of the ground state energy density, which is a function of the loop, experiences a nonanalytical point when the winding number of the corresponding loop changes. The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model, which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram. PMID:26551140
Behavior of Early Warnings near the Critical Temperature in the Two-Dimensional Ising Model
Morales, Irving O.; Landa, Emmanuel; Angeles, Carlos Calderon; Toledo, Juan C.; Rivera, Ana Leonor; Temis, Joel Mendoza; Frank, Alejandro
2015-01-01
Among the properties that are common to complex systems, the presence of critical thresholds in the dynamics of the system is one of the most important. Recently, there has been interest in the universalities that occur in the behavior of systems near critical points. These universal properties make it possible to estimate how far a system is from a critical threshold. Several early-warning signals have been reported in time series representing systems near catastrophic shifts. The proper understanding of these early-warnings may allow the prediction and perhaps control of these dramatic shifts in a wide variety of systems. In this paper we analyze this universal behavior for a system that is a paradigm of phase transitions, the Ising model. We study the behavior of the early-warning signals and the way the temporal correlations of the system increase when the system is near the critical point. PMID:26103513
Studies of hysteresis in two-dimensional kinetic Ising model using the FORC technique
NASA Astrophysics Data System (ADS)
Robb, Daniel; Novotny, Mark; Rikvold, Per Arne
2004-03-01
We describe the FORC (first order reversal curve) technique [1] for hysteresis, first developed as an experimental method to better characterize magnetic materials, and present FORC distributions for simulations of a square-lattice kinetic Ising model. To understand the simulation results, we apply a theory of magnetization reversal for the multidroplet (MD) regime [2] for homogeneous nucleation and growth, also called the Kolmogorov-Johnson-Mehl-Avrami regime. The FORC `partial hysteresis' loops exhibit different properties than those of systems with strong disorder [1]. We compare the simulation and the theory for several lattice sizes, frequencies of the external field, and temperatures. [1] C.R. Pike, A.P. Roberts, and K.L. Verosub, J. Appl. Phys. 85, 6660 (1999). [2] S.W. Sides, P.A. Rikvold, and M.A. Novotny, Phys. Rev. E 59, 2710 (1999).
Two-dimensional Ising transition through a technique from two-state opinion-dynamics models
NASA Astrophysics Data System (ADS)
Galam, Serge; Martins, André C. R.
2015-01-01
The Ising ferromagnetic model on a square lattice is revisited using the Galam unifying frame (GUF), set to investigate two-state opinion-dynamics models. When combined with Metropolis dynamics, an unexpected intermediate "dis/order" regime is found with the coexistence of two attractors associated, respectively, to an ordered and a disordered phases. The basin of attraction of initial conditions for the disordered phase attractor starts from zero size at a first critical temperature Tc 1 to embody the total landscape of initial conditions at a second critical temperature Tc 2, with Tc 1≈1.59 and Tc 2≈2.11 in J /kB units. It appears that Tc 2 is close to the Onsager result Tc≈2.27 . The transition, which is first-order-like, exhibits a vertical jump to the disorder phase at Tc 2, reminiscent of the rather abrupt vanishing of the corresponding Onsager second-order transition. However, using Glauber dynamics combined with GUF does not yield the intermediate phase and instead the expected classical mean-field transition is recovered at Tc≈3.09 . Accordingly, although the "dis/order" regime produced by the GUF-Metropolis combination is not physical, it is an intriguing result to be understood. In particular the fact that Glauber and Metropolis dynamics yield so different results using GUF needs an explanation. The possibility of extending GUF to larger clusters is discussed.
Monte Carlo investigation of critical dynamics in the three-dimensional Ising model
NASA Astrophysics Data System (ADS)
Wansleben, S.; Landau, D. P.
1991-03-01
We report the results of a Monte Carlo investigation of the (equilibrium) time-displaced correlation functions for the magnetization and energy of a simple cubic Ising model as a function of time, temperature, and lattice size. The simulations were carried out on a CDC CYBER 205 supercomputer employing a high-speed, vectorized multispin coding program and using a total of 5×1012 Monte Carlo spin-flip trials. We used L×L×L lattices with periodic boundary conditions and L as large as 96. The short-time and long-time behaviors of the correlation functions are analyzed by fits to a sum of exponential decays, and the critical exponent z for the largest relaxation time is extracted using a finite-size-scaling analysis. Our estimate z=2.04+/-0.03 resolves an intriguing contradiction in the literature; it satisfies the theoretical lower bound and is in agreement with the prediction obtained by ɛ expansion. We also consider various small systematic errors that typically occur in the analysis of relaxation functions and show how they can lead to spurious results if sufficient care is not exercised.
Two-dimensional Ising transition through a technique from two-state opinion-dynamics models.
Galam, Serge; Martins, André C R
2015-01-01
The Ising ferromagnetic model on a square lattice is revisited using the Galam unifying frame (GUF), set to investigate two-state opinion-dynamics models. When combined with Metropolis dynamics, an unexpected intermediate "dis/order" regime is found with the coexistence of two attractors associated, respectively, to an ordered and a disordered phases. The basin of attraction of initial conditions for the disordered phase attractor starts from zero size at a first critical temperature T(c1) to embody the total landscape of initial conditions at a second critical temperature T(c2), with T(c1)≈1.59 and T(c2)≈2.11 in J/k(B) units. It appears that T(c2) is close to the Onsager result T(c)≈2.27. The transition, which is first-order-like, exhibits a vertical jump to the disorder phase at T(c2), reminiscent of the rather abrupt vanishing of the corresponding Onsager second-order transition. However, using Glauber dynamics combined with GUF does not yield the intermediate phase and instead the expected classical mean-field transition is recovered at T(c)≈3.09. Accordingly, although the "dis/order" regime produced by the GUF-Metropolis combination is not physical, it is an intriguing result to be understood. In particular the fact that Glauber and Metropolis dynamics yield so different results using GUF needs an explanation. The possibility of extending GUF to larger clusters is discussed. PMID:25679571
NASA Astrophysics Data System (ADS)
Kizilirmak, Ganimet Mülazımoğlu
2015-12-01
The four-dimensional Ising model is simulated on the Creutz cellular automaton (CCA) near the infinite-lattice critical temperature for the lattice with the linear dimension 4 ⩽ L ⩽ 22. The temperature dependence of Binder parameter ( g L) are analyzed for the lattice with the linear dimension 4 ⩽ L ⩽ 22. In this study conducted highly detailed, two different types of behavior were determined as a result of varying linear lattice dimension. The infinite lattice critical temperatures are obtained to be T c = 6.6845 ± 0.0005 in interval 4 ⩽ L ⩽ 12 and T c = 6.6807 ± 0.0024 in interval 14 ⩽ L ⩽ 22. The finite and infinite lattice critical exponents for the order parameter, the magnetic susceptibility and the specific heat are computed from the results of simulations by using finite-size scaling relations. Critical linear lattice size have been identified as L = 14.
Ising and dimer models in two and three dimensions
NASA Astrophysics Data System (ADS)
Moessner, R.; Sondhi, S. L.
2003-08-01
Motivated by recent interest in 2+1 dimensional quantum dimer models, we revisit Fisher’s mapping of two-dimensional Ising models to hardcore dimer models. First, we note that the symmetry breaking transition of the ferromagnetic Ising model maps onto a non-symmetry breaking transition in dimer language—instead it becomes a deconfinement transition for test monomers. Next, we introduce a modification of Fisher’s mapping in which a second dimer model, also equivalent to the Ising model, is defined on a generically different lattice derived from the dual. In contrast to Fisher’s original mapping, this enables us to reformulate frustrated Ising models as dimer models with positive weights and we illustrate this by providing a new solution of the fully frustrated Ising model on the square lattice. Finally, by means of the modified mapping we show that a large class of three-dimensional Ising models are precisely equivalent, in the time continuum limit, to particular quantum dimer models. As Ising models in three dimensions are dual to Ising gauge theories, this further yields an exact map between the latter and the quantum dimer models. The paramagnetic phase in Ising language maps onto a deconfined, topologically ordered phase in the dimer models. Using this set of ideas, we also construct an exactly soluble quantum eight vertex model.
Montakhab, Afshin; Asadian, Ali
2010-12-15
In this paper we consider the quantum phase transition in the Ising model in the presence of a transverse field in one, two, and three dimensions from a multipartite entanglement point of view. Using exact numerical solutions, we are able to study such systems up to 25 qubits. The Meyer-Wallach measure of global entanglement is used to study the critical behavior of this model. The transition we consider is between a symmetric Greenberger-Horne-Zeilinger-like state to a paramagnetic product state. We find that global entanglement serves as a good indicator of quantum phase transition with interesting scaling behavior. We use finite-size scaling to extract the critical point as well as some critical exponents for the one- and two-dimensional models. Our results indicate that such multipartite measure of global entanglement shows universal features regardless of dimension d. Our results also provide evidence that multipartite entanglement is better suited for the study of quantum phase transitions than the much-studied bipartite measures.
Navas-Portella, Víctor; Vives, Eduard
2016-02-01
This work studies universal finite size scaling functions for the number of one-dimensional spanning avalanches in a two-dimensional (2D) disordered system with boundary conditions of different nature and different aspect ratios. To this end, we will consider the 2D random field Ising model at T=0 driven by the external field H with athermal dynamics implemented with periodic and forced boundary conditions. We have chosen a convenient scaling variable z that accounts for the deformation of the distance to the critical point caused by the aspect ratio. In addition, assuming that the dependence of the finite size scaling functions on the aspect ratio can be accounted for by an additional multiplicative factor, we have been able to collapse data for different system sizes, different aspect ratios, and different types of the boundary conditions into a single scaling function Q̂. PMID:26986310
On the dynamics of the Ising model of cooperative phenomena.
Montroll, E W
1981-01-01
A two-dimensional (and to some degree three-dimensional) version of Glauber's one-dimensional spin relaxation model is described. The model is constructed to yield the Ising model of cooperative phenomena at equilibrium. A complete hierarchy of differential equations for multispin correlation functions is constructed. Some remarks are made concerning the solution of them for the initial value problem of determining the relaxation of an initial set of spin distributions. PMID:16592955
On the Dynamics of the Ising Model of Cooperative Phenomena
NASA Astrophysics Data System (ADS)
Montroll, Elliott W.
1981-01-01
A two-dimensional (and to some degree three-dimensional) version of Glauber's one-dimensional spin relaxation model is described. The model is constructed to yield the Ising model of cooperative phenomena at equilibrium. A complete hierarchy of differential equations for multispin correlation functions is constructed. Some remarks are made concerning the solution of them for the initial value problem of determining the relaxation of an initial set of spin distributions.
On the dynamics of the Ising model of cooperative phenomena
Montroll, Elliott W.
1981-01-01
A two-dimensional (and to some degree three-dimensional) version of Glauber's one-dimensional spin relaxation model is described. The model is constructed to yield the Ising model of cooperative phenomena at equilibrium. A complete hierarchy of differential equations for multispin correlation functions is constructed. Some remarks are made concerning the solution of them for the initial value problem of determining the relaxation of an initial set of spin distributions. PMID:16592955
Sheared Ising models in three dimensions
NASA Astrophysics Data System (ADS)
Hucht, Alfred; Angst, Sebastian
2013-03-01
The nonequilibrium phase transition in sheared three-dimensional Ising models is investigated using Monte Carlo simulations in two different geometries corresponding to different shear normals [A. Hucht and S. Angst, EPL 100, 20003 (2012)]. We demonstrate that in the high shear limit both systems undergo a strongly anisotropic phase transition at exactly known critical temperatures Tc which depend on the direction of the shear normal. Using dimensional analysis, we determine the anisotropy exponent θ = 2 as well as the correlation length exponents ν∥ = 1 and ν⊥ = 1 / 2 . These results are verified by simulations, though considerable corrections to scaling are found. The correlation functions perpendicular to the shear direction can be calculated exactly and show Ornstein-Zernike behavior. Supported by CAPES-DAAD through PROBRAL as well as by the German Research Society (DFG) through SFB 616 ``Energy Dissipation at Surfaces.''
Ising model for distribution networks
NASA Astrophysics Data System (ADS)
Hooyberghs, H.; Van Lombeek, S.; Giuraniuc, C.; Van Schaeybroeck, B.; Indekeu, J. O.
2012-01-01
An elementary Ising spin model is proposed for demonstrating cascading failures (breakdowns, blackouts, collapses, avalanches, etc.) that can occur in realistic networks for distribution and delivery by suppliers to consumers. A ferromagnetic Hamiltonian with quenched random fields results from policies that maximize the gap between demand and delivery. Such policies can arise in a competitive market where firms artificially create new demand, or in a solidarity environment where too high a demand cannot reasonably be met. Network failure in the context of a policy of solidarity is possible when an initially active state becomes metastable and decays to a stable inactive state. We explore the characteristics of the demand and delivery, as well as the topological properties, which make the distribution network susceptible of failure. An effective temperature is defined, which governs the strength of the activity fluctuations which can induce a collapse. Numerical results, obtained by Monte Carlo simulations of the model on (mainly) scale-free networks, are supplemented with analytic mean-field approximations to the geometrical random field fluctuations and the thermal spin fluctuations. The role of hubs versus poorly connected nodes in initiating the breakdown of network activity is illustrated and related to model parameters.
Some Fruits of Genius: Lars Onsager and the Ising Model
NASA Astrophysics Data System (ADS)
Fisher, Michael E.
2006-03-01
The story of the exact solution of the two-dimensional Ising model by Lars Onsager in the 1940's will be sketched and some of the striking developments following from it, especially for the behavior of fluctuating interfaces, will be recounted.
Ising Model Reprogramming of a Repeat Protein's Equilibrium Unfolding Pathway.
Millership, C; Phillips, J J; Main, E R G
2016-05-01
Repeat proteins are formed from units of 20-40 aa that stack together into quasi one-dimensional non-globular structures. This modular repetitive construction means that, unlike globular proteins, a repeat protein's equilibrium folding and thus thermodynamic stability can be analysed using linear Ising models. Typically, homozipper Ising models have been used. These treat the repeat protein as a series of identical interacting subunits (the repeated motifs) that couple together to form the folded protein. However, they cannot describe subunits of differing stabilities. Here we show that a more sophisticated heteropolymer Ising model can be constructed and fitted to two new helix deletion series of consensus tetratricopeptide repeat proteins (CTPRs). This analysis, showing an asymmetric spread of stability between helices within CTPR ensembles, coupled with the Ising model's predictive qualities was then used to guide reprogramming of the unfolding pathway of a variant CTPR protein. The designed behaviour was engineered by introducing destabilising mutations that increased the thermodynamic asymmetry within a CTPR ensemble. The asymmetry caused the terminal α-helix to thermodynamically uncouple from the rest of the protein and preferentially unfold. This produced a specific, highly populated stable intermediate with a putative dimerisation interface. As such it is the first step in designing repeat proteins with function regulated by a conformational switch. PMID:26947150
Numerical tests of nucleation theories for the Ising models
NASA Astrophysics Data System (ADS)
Ryu, Seunghwa; Cai, Wei
2010-07-01
The classical nucleation theory (CNT) is tested systematically by computer simulations of the two-dimensional (2D) and three-dimensional (3D) Ising models with a Glauber-type spin flip dynamics. While previous studies suggested potential problems with CNT, our numerical results show that the fundamental assumption of CNT is correct. In particular, the Becker-Döring theory accurately predicts the nucleation rate if the correct droplet free energy function is provided as input. This validates the coarse graining of the system into a one dimensional Markov chain with the largest droplet size as the reaction coordinate. Furthermore, in the 2D Ising model, the droplet free energy predicted by CNT matches numerical results very well, after a logarithmic correction term from Langer’s field theory and a constant correction term are added. But significant discrepancies are found between the numerical results and existing theories on the magnitude of the logarithmic correction term in the 3D Ising model. Our analysis underscores the importance of correctly accounting for the temperature dependence of surface energy when comparing numerical results and nucleation theories.
Antiferromagnetic Ising Model in Hierarchical Networks
NASA Astrophysics Data System (ADS)
Cheng, Xiang; Boettcher, Stefan
2015-03-01
The Ising antiferromagnet is a convenient model of glassy dynamics. It can introduce geometric frustrations and may give rise to a spin glass phase and glassy relaxation at low temperatures [ 1 ] . We apply the antiferromagnetic Ising model to 3 hierarchical networks which share features of both small world networks and regular lattices. Their recursive and fixed structures make them suitable for exact renormalization group analysis as well as numerical simulations. We first explore the dynamical behaviors using simulated annealing and discover an extremely slow relaxation at low temperatures. Then we employ the Wang-Landau algorithm to investigate the energy landscape and the corresponding equilibrium behaviors for different system sizes. Besides the Monte Carlo methods, renormalization group [ 2 ] is used to study the equilibrium properties in the thermodynamic limit and to compare with the results from simulated annealing and Wang-Landau sampling. Supported through NSF Grant DMR-1207431.
Thermal Ising transitions in the vicinity of two-dimensional quantum critical points
NASA Astrophysics Data System (ADS)
Hesselmann, S.; Wessel, S.
2016-04-01
The scaling of the transition temperature into an ordered phase close to a quantum critical point as well as the order parameter fluctuations inside the quantum critical region provide valuable information about universal properties of the underlying quantum critical point. Here, we employ quantum Monte Carlo simulations to examine these relations in detail for two-dimensional quantum systems that exhibit a finite-temperature Ising-transition line in the vicinity of a quantum critical point that belongs to the universality class of either (i) the three-dimensional Ising model for the case of the quantum Ising model in a transverse magnetic field on the square lattice or (ii) the chiral Ising transition for the case of a half-filled system of spinless fermions on the honeycomb lattice with nearest-neighbor repulsion. While the first case allows large-scale simulations to assess the scaling predictions to a high precision in terms of the known values for the critical exponents at the quantum critical point, for the later case, we extract values of the critical exponents ν and η , related to the order parameter fluctuations, which we discuss in relation to other recent estimates from ground-state quantum Monte Carlo calculations as well as analytical approaches.
The Ising Model in Physics and Statistical Genetics
Majewski, Jacek; Li, Hao; Ott, Jurg
2001-01-01
Interdisciplinary communication is becoming a crucial component of the present scientific environment. Theoretical models developed in diverse disciplines often may be successfully employed in solving seemingly unrelated problems that can be reduced to similar mathematical formulation. The Ising model has been proposed in statistical physics as a simplified model for analysis of magnetic interactions and structures of ferromagnetic substances. Here, we present an application of the one-dimensional, linear Ising model to affected-sib-pair (ASP) analysis in genetics. By analyzing simulated genetics data, we show that the simplified Ising model with only nearest-neighbor interactions between genetic markers has statistical properties comparable to much more complex algorithms from genetics analysis, such as those implemented in the Allegro and Mapmaker-Sibs programs. We also adapt the model to include epistatic interactions and to demonstrate its usefulness in detecting modifier loci with weak individual genetic contributions. A reanalysis of data on type 1 diabetes detects several susceptibility loci not previously found by other methods of analysis. PMID:11517425
Information geometry of the ising model on planar random graphs.
Janke, W; Johnston, D A; Malmini, Ranasinghe P K C
2002-11-01
It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterization of the phase structure, particularly in the case where there are two such parameters, such as the Ising model with inverse temperature beta and external field h. In various two-parameter calculable models, the scalar curvature R of the information metric has been found to diverge at the phase transition point beta(c) and a plausible scaling relation postulated: R approximately |beta-beta(c)|(alpha-2). For spin models the necessity of calculating in nonzero field has limited analytic consideration to one-dimensional, mean-field and Bethe lattice Ising models. In this paper we use the solution in field of the Ising model on an ensemble of planar random graphs (where alpha=-1, beta=1/2, gamma=2) to evaluate the scaling behavior of the scalar curvature, and find R approximately |beta-beta(c)|(-2). The apparent discrepancy is traced back to the effect of a negative alpha. PMID:12513568
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
Some results on hyperscaling in the 3D Ising model
Baker, G.A. Jr.; Kawashima, Naoki
1995-09-01
The authors review exact studies on finite-sized 2 dimensional Ising models and show that the point for an infinite-sized model at the critical temperature is a point of nonuniform approach in the temperature-size plane. They also illuminate some strong effects of finite-size on quantities which do not diverge at the critical point. They then review Monte Carlo studies for 3 dimensional Ising models of various sizes (L = 2--100) at various temperatures. From these results they find that the data for the renormalized coupling constant collapses nicely when plotted against the correlation length, determined in a system of edge length L, divided by L. They also find that {zeta}{sub L}/L {ge} 0.26 is definitely too large for reliable studies of the critical value, g*, of the renormalized coupling constant. They have reasonable evidence that {zeta}{sub L}/L {approx} 0.1 is adequate for results that are within one percent of those for the infinite system size. On this basis, they have conducted a series of Monte Carlo calculations with this condition imposed. These calculations were made practical by the development of improved estimators for use in the Swendsen-Wang cluster method. The authors found from these results, coupled with a reversed limit computation (size increases with the temperature fixed at the critical temperature), that g* > 0, although there may well be a sharp downward drop in g as the critical temperature is approached in accord with the predictions of series analysis. The results support the validity of hyperscaling in the 3 dimensional Ising model.
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.
Exact ground states of large two-dimensional planar Ising spin glasses
NASA Astrophysics Data System (ADS)
Pardella, G.; Liers, F.
2008-11-01
Studying spin-glass physics through analyzing their ground-state properties has a long history. Although there exist polynomial-time algorithms for the two-dimensional planar case, where the problem of finding ground states is transformed to a minimum-weight perfect matching problem, the reachable system sizes have been limited both by the needed CPU time and by memory requirements. In this work, we present an algorithm for the calculation of exact ground states for two-dimensional Ising spin glasses with free boundary conditions in at least one direction. The algorithmic foundations of the method date back to the work of Kasteleyn from the 1960s for computing the complete partition function of the Ising model. Using Kasteleyn cities, we calculate exact ground states for huge two-dimensional planar Ising spin-glass lattices (up to 30002 spins) within reasonable time. According to our knowledge, these are the largest sizes currently available. Kasteleyn cities were recently also used by Thomas and Middleton in the context of extended ground states on the torus. Moreover, they show that the method can also be used for computing ground states of planar graphs. Furthermore, we point out that the correctness of heuristically computed ground states can easily be verified. Finally, we evaluate the solution quality of heuristic variants of the L. Bieche approach.
Trobo, Marta L; Albano, Ezequiel V; Binder, Kurt
2014-08-01
We present a study of the critical behavior of the Blume-Capel model with three spin states (S=±1,0) confined between parallel walls separated by a distance L where competitive surface magnetic fields act. By properly choosing the crystal field (D), which regulates the density of nonmagnetic species (S=0), such that those impurities are excluded from the bulk (where D=-∞) except in the middle of the sample [where D(M)(L/2)≠-∞], we are able to control the presence of a defect line in the middle of the sample and study its influence on the interface between domains of different spin orientations. So essentially we study an Ising model with a defect line but, unlike previous work where defect lines in Ising models were defined via weakened bonds, in the present case the defect line is due to mobile vacancies and hence involves additional entropy. In this way, by drawing phase diagrams, i.e., plots of the wetting critical temperature (T(w)) versus the magnitude of the crystal field at the middle of the sample (D(M)), we observe curves of (first-) second-order wetting transitions for (small) high values of D(M). Theses lines meet in tricritical wetting points, i.e., (T(w)(tc),D(M)(tc)), which also depend on the magnitude of the surface magnetic fields. It is found that second-order wetting transitions satisfy the scaling theory for short-range interactions, while first-order ones do not exhibit hysteresis, provided that small samples are used, since fluctuations wash out hysteretic effects. Since hysteresis is observed in large samples, we performed extensive thermodynamic integrations in order to accurately locate the first-order transition points, and a rather good agreement is found by comparing such results with those obtained just by observing the jump of the order parameter in small samples. PMID:25215741
Applying Tabu Search to the Two-Dimensional Ising Spin Glass
NASA Astrophysics Data System (ADS)
Laguna, Manuel; Laguna, Pablo
A variety of problems in statistical physics, such as Ising-like systems, can be modeled as integer programs. Physicists have relied mostly on Monte Carlo methods to find approximate solutions to these computationally difficult problems. In some cases, optimal solutions to relatively small problems have been found using standard optimization techniques, e.g., cutting plane and branch-and-bound algorithms. Motivated by the success of tabu search (TS) in finding optimal or near-optimal solutions to combinatorial optimization problems in a number of different settings, we study the application of this methodology to Ising-like systems. Particularly, we develop a TS method to find ground states of two-dimensional spin glasses. Our method performs a search at different levels of resolution in the spin lattice, and it is designed to obtain optimal or near-optimal solutions to problem instances with several different characteristics. Results are reported for computational experiments with up to 64×64 lattices.
The Worm Process for the Ising Model is Rapidly Mixing
NASA Astrophysics Data System (ADS)
Collevecchio, Andrea; Garoni, Timothy M.; Hyndman, Timothy; Tokarev, Daniel
2016-07-01
We prove rapid mixing of the worm process for the zero-field ferromagnetic Ising model, on all finite connected graphs, and at all temperatures. As a corollary, we obtain a fully-polynomial randomized approximation scheme for the Ising susceptibility, and for a certain restriction of the two-point correlation function.
The Worm Process for the Ising Model is Rapidly Mixing
NASA Astrophysics Data System (ADS)
Collevecchio, Andrea; Garoni, Timothy M.; Hyndman, Timothy; Tokarev, Daniel
2016-09-01
We prove rapid mixing of the worm process for the zero-field ferromagnetic Ising model, on all finite connected graphs, and at all temperatures. As a corollary, we obtain a fully-polynomial randomized approximation scheme for the Ising susceptibility, and for a certain restriction of the two-point correlation function.
Ising tricriticality in the extended Hubbard model with bond dimerization
NASA Astrophysics Data System (ADS)
Ejima, Satoshi; Essler, Fabian H. L.; Lange, Florian; Fehske, Holger
2016-06-01
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.
NASA Astrophysics Data System (ADS)
Miwa, Tetsuji
2013-03-01
Studies on integrable models in statistical mechanics and quantum field theory originated in the works of Bethe on the one-dimensional quantum spin chain and the work of Onsager on the two-dimensional Ising model. I will talk on the discovery in 1977 of the link between quantum field theory in the scaling limit of the two-dimensional Ising model and the theory of monodromy preserving linear ordinary differential equations. This work was the staring point of our journey with Michio Jimbo in integrable models, the journey which finally led us to the exact results on the correlation functions of quantum spin chains in 1992.
NASA Astrophysics Data System (ADS)
Horowitz, C. M.; Bab, M. A.; Mazzini, M.; Puzzo, M. L. Rubio; Saracco, G. P.
2015-10-01
The ferromagnetic Ising model with antiferromagnetic dipole interactions is investigated by means of Monte Carlo simulations, focusing on the characterization of the phase transitions between the tetragonal liquid and stripe of width h phases. The dynamic evolution of the physical observables is analyzed within the short-time regime for 0.5 ≤δ ≤1.3 , where δ is the ratio between the short-range exchange and the long-range dipole interaction constants. The obtained results for the interval 0.5 ≤δ ≤1.2 indicate that the phase transition line between the h =1 stripe and tetragonal liquid phases is continuous. This finding contributes to clarifying the controversy about the order of this transition. This controversy arises from the difficulties introduced in the simulations due to the presence of long-range dipole interactions, such as an important increase in the simulation times that limits the system size used, strong finite size effects, as well as to the existence of multiple metastable states at low temperatures. The study of the short-time dynamics of the model allows us to avoid these hindrances. Moreover, due to the fact that the finite-size effects do not significantly affect the power-law behavior exhibited in the observables within the short-time regime, the results could be attributed to those corresponding to the thermodynamic limit. As a consequence of this, a careful characterization of the critical behavior for the whole transition line is performed by giving the complete set of critical exponents.
Cyclic period-3 window in antiferromagnetic potts and Ising models on recursive lattices
NASA Astrophysics Data System (ADS)
Ananikian, N. S.; Ananikyan, L. N.; Chakhmakhchyan, L. A.
2011-09-01
The magnetic properties of the antiferromagnetic Potts model with two-site interaction and the antiferromagnetic Ising model with three-site interaction on recursive lattices have been studied. A cyclic period-3 window has been revealed by the recurrence relation method in the antiferromagnetic Q-state Potts model on the Bethe lattice (at Q < 2) and in the antiferromagnetic Ising model with three-site interaction on the Husimi cactus. The Lyapunov exponents have been calculated, modulated phases and a chaotic regime in the cyclic period-3 window have been found for one-dimensional rational mappings determined the properties of these systems.
Scaling functions in the square Ising model
NASA Astrophysics Data System (ADS)
Hassani, S.; Maillard, J.-M.
2015-03-01
We show and give the linear differential operators Lqscal of order q={{n}2}/4+n+7/8+{{(-1)}n}/8, for the integrals {{I}n}(r) which appear in the two-point correlation scaling function of Ising model \\{{F}+/- }(r)={{lim }scaling}M+/- -2 \\lt {{σ }0,0} {{σ }M,N}\\gt ={{\\sum }n}{{I}n}(r). The integrals {{I}n}(r) are given in expansion around r=0 in the basis of the formal solutions of Lqscal with transcendental combination coefficients. We find that the expression {{r}1/4}exp ({{r}2}/8) is a solution of the Painlevé VI equation in the scaling limit. Combinations of the (analytic at r=0) solutions of Lqscal sum to exp ({{r}2}/8). We show that the expression {{r}1/4}exp ({{r}2}/8) is the scaling limit of the correlation function C(N,N) and C(N,N+1). The differential Galois groups of the factors occurring in the operators Lqscal are given.
Toward an Ising model of cancer and beyond.
Torquato, Salvatore
2011-02-01
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 the research 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 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 study 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. We then describe how to incorporate angiogenesis as well as the heterogeneous and confined environment in which a tumor grows in the CA model. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently discussed. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility
Toward an Ising Model of Cancer and Beyond
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
Toward an Ising model of cancer and beyond
NASA Astrophysics Data System (ADS)
Torquato, Salvatore
2011-02-01
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 the research 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 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 study 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. We then describe how to incorporate angiogenesis as well as the heterogeneous and confined environment in which a tumor grows in the CA model. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently discussed. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility
Ising-model description of long-range correlations in DNA sequences
NASA Astrophysics Data System (ADS)
Colliva, A.; Pellegrini, R.; Testori, A.; Caselle, M.
2015-05-01
We model long-range correlations of nucleotides in the human DNA sequence using the long-range one-dimensional (1D) Ising model. We show that, for distances between 103 and 106 bp, the correlations show a universal behavior and may be described by the non-mean-field limit of the long-range 1D Ising model. This allows us to make some testable hypothesis on the nature of the interaction between distant portions of the DNA chain which led to the DNA structure that we observe today in higher eukaryotes.
Droplet model for autocorrelation functions in an Ising ferromagnet
NASA Technical Reports Server (NTRS)
Tang, Chao; Nakanishi, Hiizu; Langer, J. S.
1989-01-01
The autocorrelation function of Ising spins in an ordered phase is studied via a droplet model. Only noninteracting spherical droplets are considered. The Langevin equation which describes fluctuations in the radius of a single droplet is studied in detail. A general description of the transformation to a Fokker-Planck equations and the ways in which a spectral analysis of that equation can be used to compute the autocorrelation function is given. It is shown that the eigenvalues of the Fokker-Planck operator form (1) a continuous spectrum of relaxation rates starting from zero for d = 2, (2) a continuous spectrum with a finite gap for d = 3, and (3) a discrete spectrum for d greater than 4, where d is the spatial dimensionality. Detailed solutions for various cases are presented.
Long range Ising model for credit risk modeling
NASA Astrophysics Data System (ADS)
Molins, Jordi; Vives, Eduard
2005-07-01
Within the framework of maximum entropy principle we show that the finite-size long-range Ising model is the adequate model for the description of homogeneous credit portfolios and the computation of credit risk when default correlations between the borrowers are included. The exact analysis of the model suggest that when the correlation increases a first-order-like transition may occur inducing a sudden risk increase.
Complex zeros of the 2 d Ising model on dynamical random lattices
NASA Astrophysics Data System (ADS)
Ambjørn, J.; Anagnostopoulos, K. N.; Magnea, U.
1998-04-01
We study the zeros in the complex plane of the partition function for the Ising model coupled to 2 d quantum gravity for complex magnetic field and for complex temperature. We compute the zeros by using the exact solution coming from a two matrix model and by Monte Carlo simulations of Ising spins on dynamical triangulations. We present evidence that the zeros form simple one-dimensional patterns in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of singularities near the critical point.
Quasiparticle breakdown in the quasi-one-dimensional Ising ferromagnet CoNb2O6
NASA Astrophysics Data System (ADS)
Robinson, Neil J.; Essler, Fabian H. L.; Cabrera, Ivelisse; Coldea, Radu
2014-11-01
We present experimental and theoretical evidence that an interesting quantum many-body effect—quasiparticle breakdown—occurs in the quasi-one-dimensional spin-1/2 Ising-like ferromagnet CoNb2O6 in its paramagnetic phase at high transverse field as a result of explicit breaking of spin inversion symmetry. We propose a quantum spin Hamiltonian capturing the essential one-dimensional physics of CoNb2O6 and determine the exchange parameters of this model by fitting the calculated single-particle dispersion to the one observed experimentally in applied transverse magnetic fields [1]. We present high-resolution inelastic neutron scattering measurements of the single-particle dispersion which observe "anomalous broadening" effects over a narrow energy range at intermediate energies. We propose that this effect originates from the decay of the one particle mode into two-particle states. This decay arises from (i) a finite overlap between the one-particle dispersion and the two-particle continuum in a narrow energy-momentum range and (ii) a small misalignment of the applied field away from the direction perpendicular to the Ising axis in the experiments, which allows for nonzero matrix elements for decay by breaking the Z2 spin inversion symmetry of the Hamiltonian.
Critical properties of a two-dimensional Ising magnet with quasiperiodic interactions
NASA Astrophysics Data System (ADS)
Alves, G. A.; Vasconcelos, M. S.; Alves, T. F. A.
2016-04-01
We address the study of quasiperiodic interactions on a square lattice by using an Ising model with ferromagnetic and antiferromagnetic exchange interactions following a quasiperiodic Fibonacci sequence in both directions of a square lattice. We applied the Monte Carlo method, together with the Metropolis algorithm, to calculate the thermodynamic quantities of the system. We obtained the Edwards-Anderson order parameter qEA, the magnetic susceptibility χ , and the specific heat c in order to characterize the universality class of the phase transition. We also use the finite size scaling method to obtain the critical temperature of the system and the critical exponents β ,γ , and ν . In the low-temperature limit we obtained a spin-glass phase with critical temperature around Tc≈2.274 , and the critical exponents β ,γ , and ν , indicating that the quasiperiodic order induces a change in the universality class of the system. Also, we discovered a spin-glass ordering in a two-dimensional system which is rare and, as far as we know, the unique example is an under-frustrated Ising model.
Critical properties of a two-dimensional Ising magnet with quasiperiodic interactions.
Alves, G A; Vasconcelos, M S; Alves, T F A
2016-04-01
We address the study of quasiperiodic interactions on a square lattice by using an Ising model with ferromagnetic and antiferromagnetic exchange interactions following a quasiperiodic Fibonacci sequence in both directions of a square lattice. We applied the Monte Carlo method, together with the Metropolis algorithm, to calculate the thermodynamic quantities of the system. We obtained the Edwards-Anderson order parameter q_{EA}, the magnetic susceptibility χ, and the specific heat c in order to characterize the universality class of the phase transition. We also use the finite size scaling method to obtain the critical temperature of the system and the critical exponents β,γ, and ν. In the low-temperature limit we obtained a spin-glass phase with critical temperature around T_{c}≈2.274, and the critical exponents β,γ, and ν, indicating that the quasiperiodic order induces a change in the universality class of the system. Also, we discovered a spin-glass ordering in a two-dimensional system which is rare and, as far as we know, the unique example is an under-frustrated Ising model. PMID:27176258
Two-dimensional frustrated Ising network as an eigenvalue problem
NASA Astrophysics Data System (ADS)
Blackman, J. A.
1982-11-01
The Pfaffian method is used to study the square frustrated Ising network. The formalism is adapted in order to develop a relation with the problem of excitations in random alloys. It is shown that the counterpart of frustrated plaquettes are local modes within a band gap. Properties of the local modes are examined, including questions of gauge invariance and duality. Numerical calculations are done to investigate the way in which the local modes broaden into an impurity band.
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).
Interacting damage models mapped onto ising and percolation models
Toussaint, Renaud; Pride, Steven R.
2004-03-23
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 the 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 damage model
Interacting damage models mapped onto Ising and percolation models.
Toussaint, Renaud; Pride, Steven R
2005-04-01
We introduce a class of damage models on regular lattices with isotropic interactions between the broken cells of the lattice. Quasi-static 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 the system exceeds the surface-energy barrier necessary to break the cell. By direct integration over all possible realizations of the quenched disorder, we obtain the probability distribution of each damage configuration at any level of the imposed external deformation. We 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, we show that damage models with global load sharing are isomorphic to standard percolation theory and that damage models with a 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. We 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, we 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 damage model to standard
An Ising model of transcription polarity in bacterial chromosomes
NASA Astrophysics Data System (ADS)
Baran, Robert H.; Ko, Hanseok
2006-04-01
Bacterial genes form clusters of the same transcription polarity and typically exhibit a preference to be coded on the leading strand of replication. An Ising model is proposed to quantify these two phenomena by analogy to the behavior of magnetic dipoles (spins) in a one-dimensional lattice. Corresponding to magnetic forces that co-orient adjacent spins and align them with an externally applied field, we imagine pseudo-forces that influence transcription polarity. Bonds of uniform strength {1}/{2} J between adjacent sites will model the adhesive (or repulsive) interactions while a polarity entraining force of strength H has the direction of replication. Ten bacterial chromosomes are reduced to spin configurations from which the model parameters are estimated by the method of maximum likelihood under the assumption of thermal equilibrium, following the application of established methods to locate replication origins and termini. χ 2-tests show that the model fits the data well in about half the cases but cluster size exhibits excess variance in general. These findings lead to a speculative interpretation of the pseudo-forces as the net effects of numerous insertions and deletions that succeed or fail according to their impact on the motions of enzymatic complexes involved in replication and transcription.
The gonihedric paradigm extension of the Ising model
NASA Astrophysics Data System (ADS)
Savvidy, George
2015-11-01
In this paper we review a recently suggested generalization of the Feynman path integral to an integral over random surfaces. The proposed action is proportional to the linear size of the random surfaces and is called gonihedric. The convergence and the properties of the partition function are analyzed. The model can also be formulated as a spin system with identical partition functions. The spin system represents a generalization of the Ising model with ferromagnetic, antiferromagnetic and quartic interactions. Higher symmetry of the model allows to construct dual spin systems in three and four dimensions. In three dimensions the transfer matrix describes the propagation of closed loops and we found its exact spectrum. It is a unique exact solution of the three-dimensional statistical spin system. In three and four dimensions, the system exhibits the second-order phase transitions. The gonihedric spin systems have exponentially degenerated vacuum states separated by the potential barriers and can be used as a storage of binary information.
Phase transitions in Ising models on directed networks.
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. PMID:26651748
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.
Topological defects on the lattice: I. The Ising model
NASA Astrophysics Data System (ADS)
Aasen, David; Mong, Roger S. K.; Fendley, Paul
2016-09-01
In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect commutation relations, cousins of the Yang–Baxter equation. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. In this part I, we focus on the simplest example, the Ising model. We define lattice spin-flip and duality defects and their branching, and prove they are topological. One useful consequence is a simple implementation of Kramers–Wannier duality on the torus and higher genus surfaces by using the fusion of duality defects. We use these topological defects to do simple calculations that yield exact properties of the conformal field theory describing the continuum limit. For example, the shift in momentum quantization with duality-twisted boundary conditions yields the conformal spin 1/16 of the chiral spin field. Even more strikingly, we derive the modular transformation matrices explicitly and exactly.
Duality Between Spin Networks and the 2D Ising Model
NASA Astrophysics Data System (ADS)
Bonzom, Valentin; Costantino, Francesco; Livine, Etera R.
2016-06-01
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories that couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.
Analytical properties of the anisotropic cubic Ising model
Hansel, D.; Maillard, J.M.; Oitmaa, J.; Velgakis, M.J.
1987-07-01
The authors combine an exact functional relation, the inversion relation, with conventional high-temperature expansions to explore the analytic properties of the anisotropic Ising model on both the square and simple cubic lattice. In particular, they investigate the nature of the singularities that occur in partially resummed expansions of the partition function and of the susceptibility.
Periodic Striped Ground States in Ising Models with Competing Interactions
NASA Astrophysics Data System (ADS)
Giuliani, Alessandro; Seiringer, Robert
2016-06-01
We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than d + 1, with d the space dimension, this happens for all values of J smaller than a critical value J c (p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for p > 2d and J in a left neighborhood of J c (p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes (d = 2) or slabs (d = 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.
Constrained variational problem with applications to the Ising model
NASA Astrophysics Data System (ADS)
Schonmann, Roberto H.; Shlosman, Senya B.
1996-06-01
We continue our study of the behavior of the two-dimensional nearest neighbor ferromagnetic Ising model under an external magnetic field h, initiated in our earlier work. We strengthen further a result previously proven by Martirosyan at low enough temperature, which roughly states that for finite systems with (-)-boundary conditions under a positive external field, the boundary effect dominates in the system if the linear size of the system is of order B/h with B small enough, while if B is large enough, then the external field dominates in the system. In our earlier work this result was extended to every subcritical value of the temperature. Here for every subcritical value of the temperature we show the existence of a critical value B 0 (T) which separates the two regimes specified above. We also find the asymptotic shape of the region occupied by the (+)-phase in the second regime, which turns out to be a "squeezed Wulff shape". The main step in our study is the solution of the variational problem of finding the curve minimizing the Wulff functional, which curve is constrained to the unit square. Other tools used are the results and techniques developed to study large deviations for the block magnetization in the absence of the magnetic field, extended to all temperatures below the critical one.
Critical behavior of the Ising model on random fractals
NASA Astrophysics Data System (ADS)
Monceau, Pascal
2011-11-01
We study the critical behavior of the Ising model in the case of quenched disorder constrained by fractality on random Sierpinski fractals with a Hausdorff dimension df≃1.8928. This is a first attempt to study a situation between the borderline cases of deterministic self-similarity and quenched randomness. Intensive Monte Carlo simulations were carried out. Scaling corrections are much weaker than in the deterministic cases, so that our results enable us to ensure that finite-size scaling holds, and that the critical behavior is described by a new universality class. The hyperscaling relation is compatible with an effective dimension equal to the Hausdorff one; moreover the two eigenvalues exponents of the renormalization flows are shown to be different from the ones calculated from ɛ expansions, and from the ones obtained for fourfold symmetric deterministic fractals. Although the space dimensionality is not integer, lack of self-averaging properties exhibits some features very close to the ones of a random fixed point associated with a relevant disorder.
The Ising Model on a Quenched Ensemble of c=-5 Gravity Graphs
NASA Astrophysics Data System (ADS)
Anagnostopoulos, K. N.; Bialas, P.; Thorleifsson, G.
1999-02-01
We study with Monte Carlo methods an ensemble of c=-5 gravity graphs, generated by coupling a conformal field theory with central charge c=-5 to two-dimensional quantum gravity. We measure the fractal properties of the ensemble, such as the string susceptibility exponent γ s and the intrinsic fractal dimension d H. We find γ s=-1.5(1) and d H=3.36(4), in reasonable agreement with theoretical predictions. In addition, we study the critical behavior of an Ising model on a quenched ensemble of the c=-5 graphs and show that it agrees, within numerical accuracy, with theoretical predictions for the critical behavior of an Ising model coupled dynamically to two-dimensional quantum gravity, with a total central charge of the matter sector c=-5.
NASA Astrophysics Data System (ADS)
Neto, Minos A.; de Sousa, J. Ricardo; Padilha, Igor T.; Rodriguez Salmon, Octavio D.; Roberto Viana, J.; Dinóla Neto, F.
2016-06-01
We study the three-dimensional antiferromagnetic Ising model in both uniform longitudinal (H) and transverse (Ω) magnetic fields by using the effective-field theory (EFT) with finite cluster N = 1 spin (EFT-1). We analyzed the behavior of the magnetic susceptibility to investigate the reentrant phenomena that we have seen in the same phase diagram previously obtained in other papers. Our results shows the presence of two divergences in the susceptibility that indicates the existence of a reentrant behavior.
Two Dimensional Ising Superconductivity in Gated MoS2
NASA Astrophysics Data System (ADS)
Yuan, Noah; Lu, Jianming; Law, Kam Tuen; Zheliuk, Oleksandr; Leermakers, Inge; Zeitler, Ulrich; Ye, Jianting
The Zeeman effect, which is usually considered to be detrimental to superconductivity, can surprisingly protect the superconducting states created by gating a layered transition metal dichalcogenide. This effective Zeeman field, which is originated from intrinsic spin orbit coupling induced by breaking in-plane inversion symmetry, can reach nearly a hundred Tesla in magnitude. It strongly pins the spin orientation of the electrons to the out-of-plane directions and protects the superconductivity from being destroyed by an in-plane external magnetic field. In magnetotransport experiments of ionic-gate MoS2 transistors, where gating prepares individual superconducting state with different carrier doping, we indeed observe a spin-protected superconductivity by measuring an in-plane critical field Bc 2 far beyond the Pauli paramagnetic limit. The gating-enhanced Bc 2 is more than an order of magnitude larger compared to the bulk superconducting phases where the effective Zeeman field is weakened by interlayer coupling. Our study gives the first experimental evidence of an Ising superconductor, in which spins of the pairing electrons are strongly pinned by an effective Zeeman field.
NASA Astrophysics Data System (ADS)
Cabrera, Ivelisse; Thompson, Jordan; Coldea, Radu; Robinson, Neil; Essler, Fabian; Prabhakaran, Dharmalingam; Bewley, Robert; Guidi, Tatiana
2013-03-01
The Ising chain in a transverse magnetic field is one of the canonical examples of a quantum phase transition. We have recently realized this model experimentally in the quasi-one-dimensional (1D) Ising-like ferromagnet CoNb2O6. Here, we present single-crystal inelastic neutron scattering measurements of the magnetic dispersion relations in the full three-dimensional (3D) Brillouin zone for magnetic fields near the critical point and in the high field paramagnetic phase. We explore the gap dependence as a function of field and quantify the cross-over to 3D physics at the lowest energies due to the finite interchain couplings. We parametrize the dispersion relations in the high-field paramagnetic phase to a spin wave model to quantify the sub-leading terms in the spin Hamiltonian beyond the dominant 1D Ising exchange.
A MATLAB GUI to study Ising model phase transition
NASA Astrophysics Data System (ADS)
Thornton, Curtislee; Datta, Trinanjan
We have created a MATLAB based graphical user interface (GUI) that simulates the single spin flip Metropolis Monte Carlo algorithm. The GUI has the capability to study temperature and external magnetic field dependence of magnetization, susceptibility, and equilibration behavior of the nearest-neighbor square lattice Ising model. Since the Ising model is a canonical system to study phase transition, the GUI can be used both for teaching and research purposes. The presence of a Monte Carlo code in a GUI format allows easy visualization of the simulation in real time and provides an attractive way to teach the concept of thermal phase transition and critical phenomena. We will also discuss the GUI implementation to study phase transition in a classical spin ice model on the pyrochlore lattice.
Information cascade, Kirman's ant colony model, and kinetic Ising model
NASA Astrophysics Data System (ADS)
Hisakado, Masato; Mori, Shintaro
2015-01-01
In this paper, we discuss a voting model in which voters can obtain information from a finite number of previous voters. There exist three groups of voters: (i) digital herders and independent voters, (ii) analog herders and independent voters, and (iii) tanh-type herders. In our previous paper Hisakado and Mori (2011), we used the mean field approximation for case (i). In that study, if the reference number r is above three, phase transition occurs and the solution converges to one of the equilibria. However, the conclusion is different from mean field approximation. In this paper, we show that the solution oscillates between the two states. A good (bad) equilibrium is where a majority of r select the correct (wrong) candidate. In this paper, we show that there is no phase transition when r is finite. If the annealing schedule is adequately slow from finite r to infinite r, the voting rate converges only to the good equilibrium. In case (ii), the state of reference votes is equivalent to that of Kirman's ant colony model, and it follows beta binomial distribution. In case (iii), we show that the model is equivalent to the finite-size kinetic Ising model. If the voters are rational, a simple herding experiment of information cascade is conducted. Information cascade results from the quenching of the kinetic Ising model. As case (i) is the limit of case (iii) when tanh function becomes a step function, the phase transition can be observed in infinite size limit. We can confirm that there is no phase transition when the reference number r is finite.
Phase transition of the Ising model on a fractal lattice.
Genzor, Jozef; Gendiar, Andrej; Nishino, Tomotoshi
2016-01-01
The phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a factor of 4. The free energy and the spontaneous magnetization of the system are obtained by means of the higher-order tensor renormalization group method. The system exhibits the order-disorder phase transition, where the critical indices are different from those of the square-lattice Ising model. An exponential decay is observed in the density-matrix spectrum even at the critical point. It is possible to interpret that the system is less entangled because of the fractal geometry. PMID:26871057
Precision islands in the Ising and O( N ) models
NASA Astrophysics Data System (ADS)
Kos, Filip; Poland, David; Simmons-Duffin, David; Vichi, Alessandro
2016-08-01
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 ɛ , λ σσɛ , λ ɛɛɛ ) = (0 .5181489(10) , 1 .412625(10) , 1 .0518537(41) , 1 .532435(19) , give the most precise determinations of these quantities to date.
Phase transition of the Ising model on a fractal lattice
NASA Astrophysics Data System (ADS)
Genzor, Jozef; Gendiar, Andrej; Nishino, Tomotoshi
2016-01-01
The phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a factor of 4. The free energy and the spontaneous magnetization of the system are obtained by means of the higher-order tensor renormalization group method. The system exhibits the order-disorder phase transition, where the critical indices are different from those of the square-lattice Ising model. An exponential decay is observed in the density-matrix spectrum even at the critical point. It is possible to interpret that the system is less entangled because of the fractal geometry.
Ising model observables and non-backtracking walks
Helmuth, Tyler
2014-08-15
This paper presents an alternative proof of the connection between the partition function of the Ising model on a finite graph G and the set of non-backtracking walks on G. The techniques used also give formulas for spin-spin correlation functions in terms of non-backtracking walks. The main tools used are Viennot's theory of heaps of pieces and turning numbers on surfaces.
Magnetization of the Ising model on the generalized checkerboard lattice
NASA Astrophysics Data System (ADS)
Lin, K. Y.; Wu, F. Y.
1988-08-01
We consider the Ising model on the generalized checkerboard lattice. Using a recent result by Baxter and Choy, we derive exact expressions for the magnetization of nodal spins at two values of the magnetic field, H=0 and H=i1/2 πkT. Our results are given in terms of Boltzmann weights of a unit cell of the checkerboard lattice without specifying its cell structures.
NASA Technical Reports Server (NTRS)
Fitzenreiter, R. J.; Scudder, J. D.
1981-01-01
A computer package which produces contour plots of the three dimensional electron distribution function measured by an electron spectrometer aboard ISEE-1 is described. Examples of the contour plots and an explanation of how to use the program, including the necessary computer code for running the program on the GSFC 360/91 computer is presented. The method by which the discrete measurements of the distribution function, given by points on the four dimensional surface are synthesized into a smooth surface in a three dimensional space which can be contoured is described. The velocity components are parallel and perpendicular to the magnetic field, respectively, in the proper frame of the electrons.
Singularities of the Partition Function for the Ising Model Coupled to 2D Quantum Gravity
NASA Astrophysics Data System (ADS)
Ambjørn, J.; Anagnostopoulos, K. N.; Magnea, U.
We study the zeros in the complex plane of the partition function for the Ising model coupled to 2D quantum gravity for complex magnetic field and real temperature, and for complex temperature and real magnetic field, respectively. We compute the zeros by using the exact solution coming from a two-matrix model and by Monte-Carlo simulations of Ising spins on dynamical triangulations. We present evidence that the zeros form simple one-dimensional curves in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of the singularities near the critical point. Despite the small size of the systems studied, we can obtain a reasonable estimate of the (known) critical exponents.
Rényi information flow in the Ising model with single-spin dynamics.
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. PMID:25615223
Rényi information flow in the Ising model with single-spin dynamics
NASA Astrophysics Data System (ADS)
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.
Lateral critical Casimir force in two-dimensional inhomogeneous Ising strip. Exact results.
Nowakowski, Piotr; Napiórkowski, Marek
2016-06-01
We consider two-dimensional Ising strip bounded by two planar, inhomogeneous walls. The inhomogeneity of each wall is modeled by a magnetic field acting on surface spins. It is equal to +h1 except for a group of N1 neighboring surface spins where it is equal to -h1. The inhomogeneities of the upper and lower wall are shifted with respect to each other by a lateral distance L. Using exact diagonalization of the transfer matrix, we study both the lateral and normal critical Casimir forces as well as magnetization profiles for different temperature regimes: below the wetting temperature, between the wetting and the critical temperature, and above the critical temperature. The lateral critical Casimir force acts in the direction opposite to the shift L, and the excess normal force is always attractive. Upon increasing the shift L we observe, depending on the temperature regime, three different scenarios of breaking of the capillary bridge of negative magnetization connecting the inhomogeneities of the walls across the strip. As long as there exists a capillary bridge in the system, the magnitude of the excess total critical Casimir force is almost constant, with its direction depending on L. By investigating the bridge morphologies we have found a relation between the point at which the bridge breaks and the inflection point of the force. We provide a simple argument that some of the properties reported here should also hold for different models of the strip with the same type of inhomogeneity. PMID:27276962
Trobo, Marta L; Albano, Ezequiel V; Binder, Kurt
2016-05-01
As a simplified model of a liquid nanostripe adsorbed on a chemically structured substrate surface, a two-dimensional Ising system with two boundaries at which surface fields act is studied. At the upper boundary, the surface field is uniformly negative, while at the lower boundary (a distance L apart), the surface field is negative only outside a range of extension b, where a positive surface stabilizes a droplet of the phase with positive magnetization for temperatures T exceeding the critical temperature T_{w} of the wetting transition of this model. We investigate the local order parameter profiles across the droplet, both in the directions parallel and perpendicular to the substrate, varying both b and T. Also, precursor effects to droplet formation as T approaches T_{w} from below are studied. In accord with theoretical predictions, for T>T_{w} the droplet is found to have the shape of a semiellipse, where the width (distance of the interface from the substrate) scale is proportional to b (b^{1/2}). So, the area of the droplet is proportional to b^{3/2}, and the temperature dependence of the corresponding prefactor, which also involves the interfacial stiffness, is studied. PMID:27300962
NASA Astrophysics Data System (ADS)
Trobo, Marta L.; Albano, Ezequiel V.; Binder, Kurt
2016-05-01
As a simplified model of a liquid nanostripe adsorbed on a chemically structured substrate surface, a two-dimensional Ising system with two boundaries at which surface fields act is studied. At the upper boundary, the surface field is uniformly negative, while at the lower boundary (a distance L apart), the surface field is negative only outside a range of extension b , where a positive surface stabilizes a droplet of the phase with positive magnetization for temperatures T exceeding the critical temperature Tw of the wetting transition of this model. We investigate the local order parameter profiles across the droplet, both in the directions parallel and perpendicular to the substrate, varying both b and T . Also, precursor effects to droplet formation as T approaches Tw from below are studied. In accord with theoretical predictions, for T >Tw the droplet is found to have the shape of a semiellipse, where the width (distance of the interface from the substrate) scale is proportional to b (b1 /2). So, the area of the droplet is proportional to b3 /2, and the temperature dependence of the corresponding prefactor, which also involves the interfacial stiffness, is studied.
Self-overlap as a method of analysis in Ising models.
Ferrera, A; Luque, B; Lacasa, L; Valero, E
2007-06-01
The damage spreading (DS) method provided a useful tool to obtain analytical results of the thermodynamics and stability of the two-dimensional (2D) Ising model--amongst many others--but it suffered both from ambiguities in its results and from large computational costs. In this paper we propose an alternative method, the so-called self-overlap method, based on the study of correlation functions measured at subsequent time steps as the system evolves towards its equilibrium. Applying Markovian and mean-field approximations to a 2D Ising system we obtain both analytical and numerical results on the thermodynamics that agree with the expected behavior. We also provide some analytical results on the stability of the system. Since only a single replica of the system needs to be studied, this method would seem to be free from the ambiguities that afflicted the DS method. It also seems to be numerically more efficient and analytically simpler. PMID:17677216
Interface localization in the 2D Ising model with a driven line
NASA Astrophysics Data System (ADS)
Cohen, O.; Mukamel, D.
2016-04-01
We study the effect of a one-dimensional driving field on the interface between two coexisting phases in a two dimensional model. This is done by considering an Ising model on a cylinder with Glauber dynamics in all sites and additional biased Kawasaki dynamics in the central ring. Based on the exact solution of the two-dimensional Ising model, we are able to compute the phase diagram of the driven model within a special limit of fast drive and slow spin flips in the central ring. The model is found to exhibit two phases where the interface is pinned to the central ring: one in which it fluctuates symmetrically around the central ring and another where it fluctuates asymmetrically. In addition, we find a phase where the interface is centered in the bulk of the system, either below or above the central ring of the cylinder. In the latter case, the symmetry breaking is ‘stronger’ than that found in equilibrium when considering a repulsive potential on the central ring. This equilibrium model is analyzed here by using a restricted solid-on-solid model.
The sign-factor of the 3D Ising model on dual BCC lattice
NASA Astrophysics Data System (ADS)
Khachatryan, Sh.; Sedrakyan, A.
2002-01-01
We modify the two-dimensional model for the sign-factor of the regular 3D Ising model (3DIM) presented by Kavalov and Sedrakyan (Phys. Lett. 173B (1986) 449 and Nucl. Phys. 285B (1987) 264) for the case of dual to body centered cubic (DBCC) three-dimensional lattice. The advantage of this lattice is in an absence of self-intersections of the two-dimensional surfaces embedded there. We investigate simpler case of the model with scalar fermions (instead of SU(2) needed for 3DIM) and have found it's spectrum, which appeared to be massless. We reformulate the model by use of R-matrix formalism and a new interesting structure appears in a necessity to introduce three-particle R(3)ijk-matrices. We formulate the integrability property of the model for more general case.
NASA Technical Reports Server (NTRS)
Zhuang, H. C.; Russell, C. T.; Smith, E. J.; Gosling, J. T.
1981-01-01
The reported investigation is concerned with the propagation of the interplanetary shock waves in the solar wind and their three-dimensional interaction with the bow shock and magnetosheath. Formulae are deduced to predict the new position and orientation of the bow shock front after the interaction. To test the understanding of the interplanetary portion of the shock propagation, the obtained results are compared with observations on August 18, 1978, when both ISEE 1 and ISEE 3 were in the solar wind. Two examples of an interplanetary shock wave penetrating into the magnetosphere on October 4, 1978, and August 27, 1978, are examined, taking into account a simple model of the magnetosheath. The results agree with the observed values of the ISEE satellite data within experimental uncertainties.
Ising-like models on arbitrary graphs: The Hadamard way
NASA Astrophysics Data System (ADS)
Mosseri, Rémy
2015-01-01
We propose a generic framework to describe classical Ising-like models defined on arbitrary graphs. The energy spectrum is shown to be the Hadamard transform of a suitably defined sparse "coding" vector associated with the graph. We expect that the existence of a fast Hadamard transform algorithm (used, for instance, in image compression processes), together with the sparseness of the coding vector, may provide ways to fasten the spectrum computation. Applying this formalism to regular graphs, such as hypercubic graphs, we obtain a simple recurrence relation for the spectrum, which significantly speeds up its determination. First attempts to analyze partition functions and transfer matrices are also presented.
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.
Oscillating hysteresis in the q -neighbor Ising model
NASA Astrophysics Data System (ADS)
JÈ©drzejewski, Arkadiusz; Chmiel, Anna; Sznajd-Weron, Katarzyna
2015-11-01
We modify the kinetic Ising model with Metropolis dynamics, allowing each spin to interact only with q spins randomly chosen from the whole system, which corresponds to the topology of a complete graph. We show that the model with q ≥3 exhibits a phase transition between ferromagnetic and paramagnetic phases at temperature T*, which linearly increases with q . Moreover, we show that for q =3 the phase transition is continuous and that it is discontinuous for larger values of q . For q >3 , the hysteresis exhibits oscillatory behavior—expanding for even values of q and shrinking for odd values of q . Due to the mean-field-like nature of the model, we are able to derive the analytical form of transition probabilities and, therefore, calculate not only the probability density function of the order parameter but also precisely determine the hysteresis and the effective potential showing stable, unstable, and metastable steady states. Our results show that a seemingly small modification of the kinetic Ising model leads not only to the switch from a continuous to a discontinuous phase transition, but also to an unexpected oscillating behavior of the hysteresis and a puzzling phenomenon for q =5 , which might be taken as evidence for the so-called mixed-order phase transition.
Oscillating hysteresis in the q-neighbor Ising model.
Jȩdrzejewski, Arkadiusz; Chmiel, Anna; Sznajd-Weron, Katarzyna
2015-11-01
We modify the kinetic Ising model with Metropolis dynamics, allowing each spin to interact only with q spins randomly chosen from the whole system, which corresponds to the topology of a complete graph. We show that the model with q≥3 exhibits a phase transition between ferromagnetic and paramagnetic phases at temperature T*, which linearly increases with q. Moreover, we show that for q=3 the phase transition is continuous and that it is discontinuous for larger values of q. For q>3, the hysteresis exhibits oscillatory behavior-expanding for even values of q and shrinking for odd values of q. Due to the mean-field-like nature of the model, we are able to derive the analytical form of transition probabilities and, therefore, calculate not only the probability density function of the order parameter but also precisely determine the hysteresis and the effective potential showing stable, unstable, and metastable steady states. Our results show that a seemingly small modification of the kinetic Ising model leads not only to the switch from a continuous to a discontinuous phase transition, but also to an unexpected oscillating behavior of the hysteresis and a puzzling phenomenon for q=5, which might be taken as evidence for the so-called mixed-order phase transition. PMID:26651645
Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study
Dusuel, Sebastien; Kamfor, Michael; Schmidt, Kai Phillip; Thomale, Ronny; Vidal, Julien
2010-02-01
We analyze the properties of low-energy bound states in the transverse-field Ising model and in the XXZ model on the square lattice. To this end, we develop an optimized implementation of perturbative continuous unitary transformations. The Ising model is studied in the small-field limit which is found to be a special case of the toric code model in a magnetic field. To analyze the XXZ model, we perform a perturbative expansion about the Ising limit in order to discuss the fate of the elementary magnon excitations when approaching the Heisenberg point.
Phase diagram and critical behavior of the antiferromagnetic Ising model in an external field
NASA Astrophysics Data System (ADS)
Jeferson Lourenço, Bruno; Dickman, Ronald
2016-03-01
We study the critical properties of the antiferromagnetic spin-1/2 Ising model in an external field on the square lattice. Using tomographic entropic sampling, a flat-histogram simulation method, we estimate the number of configurations, Ω , and related microcanonical averages in the energy-magnetization space, for system sizes L = 10-30. The critical line and exponents are calculated using finite-size scaling analysis in the temperature-external field plane. With these estimates in hand, we perform detailed studies of critical behavior using Metropolis sampling of larger systems (L≤slant 320 ). These results are compared to several approximate theoretical methods. Our estimates of critical exponents and Binder’s reduced fourth cumulant along the critical line are in very good agreement with their respective literature values for the two-dimensional Ising universality class. We verify as well that the specific heat scales ˜ \\ln L along the critical line, as expected for an Ising-like critical point.
The Ising Model Applied on Chronification of Pain
2016-01-01
This is a hypothesis-article suggesting an entirely new framework for understanding and treating longstanding pain. Most medical and psychological models are described with boxes and arrows. Such models are of little clinical and explanatory use when describing the phenomenon of chronification of pain due to unknown causes. To date no models that have been provided - and tested in a scientific satisfactory way - lays out a plan for specific assessment due to a specific causal explanation, and in the end serves the clinicians, patients and researcher with tools on how to address the specific pain condition to every individual pain patient's condition. By applying the Ising model (from physics) on the phenomenon of chronification of pain, one is able to detangle all these factors, and thus have a model that both suggests an explanation of the condition and outlines how one might target the treatment of chronic pain patients with the use of network science. PMID:26398917
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.
Three-spin interaction Ising model with a nondegenerate ground state at zero applied field
NASA Astrophysics Data System (ADS)
Bidaux, R.; Boccara, N.; Forgàcs, G.
1986-10-01
The field-temperature phase diagram of a two-dimensional, three-spin interaction Ising model is studied using two different methods: mean field approximation and numerical transfer matrix techniques. The former leads to a rather rich phase diagram in which two separate phases with different symmetries can be found, and which presents first-order transition lines, a triple point, and a critical end point, like the solid-liquid-gas phase diagram of a pure compound. The numerical transfer matrix study confirms part of these results, but does not clearly evidence the existence of the less symmetric phase.
Saturation field entropies of antiferromagnetic Ising models: Ladders and the kagome lattice
NASA Astrophysics Data System (ADS)
Varma, Vipin Kerala
2013-10-01
Saturation field entropies of antiferromagnetic Ising models on quasi-one-dimensional lattices (ladders) and the kagome lattice are calculated. The former is evaluated exactly by constructing the corresponding transfer matrices, while the latter calculation uses Binder's algorithm for efficiently and exactly computing the partition function of over 1300 spins to give Skag/kB=0.393589(6). We comment on the relation of the kagome lattice to the experimental situation in the spin-ice compound Dy2Ti2O7.
Quantum cluster algorithm for frustrated Ising models in a transverse field
NASA Astrophysics Data System (ADS)
Biswas, Sounak; Rakala, Geet; Damle, Kedar
2016-06-01
Working within the stochastic series expansion framework, we introduce and characterize a plaquette-based quantum cluster algorithm for quantum Monte Carlo simulations of transverse field Ising models with frustrated Ising exchange interactions. As a demonstration of the capabilities of this algorithm, we show that a relatively small ferromagnetic next-nearest-neighbor coupling drives the transverse field Ising antiferromagnet on the triangular lattice from an antiferromagnetic three-sublattice ordered state at low temperature to a ferrimagnetic three-sublattice ordered state.
Planar ordering in the plaquette-only gonihedric Ising model
NASA Astrophysics Data System (ADS)
Mueller, Marco; Janke, Wolfhard; Johnston, Desmond A.
2015-05-01
In this paper we conduct a careful multicanonical simulation of the isotropic 3d plaquette ("gonihedric") Ising model and confirm that a planar, fuki-nuke type order characterises the low-temperature phase of the model. From consideration of the anisotropic limit of the model we define a class of order parameters which can distinguish the low- and high-temperature phases in both the anisotropic and isotropic cases. We also verify the recently voiced suspicion that the order parameter like behaviour of the standard magnetic susceptibility χm seen in previous Metropolis simulations was an artefact of the algorithm failing to explore the phase space of the macroscopically degenerate low-temperature phase. χm is therefore not a suitable order parameter for the model.
Emergent Ising degrees of freedom in the J1-J2-J3 model for the iron tellurides
NASA Astrophysics Data System (ADS)
Zhang, Guanghua; Fernandes, Rafael; Flint, Rebecca
The iron-telluride family of superconductors form a double-stripe [ Q = (π / 2 , π / 2) ] magnetic order, which can be 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. Via their coupling to the lattice, they give rise to a monoclinic distortion and to two non-uniform lattice distortions with wave-vector (π , π) . Because the ground state is four-fold degenerate (mod rotations in spin space), only two of these Ising order parameters are independent. Here we introduce an effective field theory to treat all Ising order parameters, as well as magnetic order. All three transitions (corresponding to the condensations of two Ising 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.
Driven-dissipative Ising model: Mean-field solution
NASA Astrophysics Data System (ADS)
Goldstein, G.; Aron, C.; Chamon, C.
2015-11-01
We study the fate of the Ising model and its universal properties when driven by a rapid periodic drive and weakly coupled to a bath at equilibrium. The far-from-equilibrium steady-state regime is accessed by means of a Floquet mean-field approach. We show that, depending on the details of the bath, the drive can strongly renormalize the critical temperature to higher temperatures, modify the critical exponents, or even change the nature of the phase transition from second to first order after the emergence of a tricritical point. Moreover, by judiciously selecting the frequency of the field and by engineering the spectrum of the bath, one can drive a ferromagnetic Hamiltonian to an antiferromagnetically ordered phase and vice versa.
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.
Reentrance of disorder in the anisotropic shuriken Ising model
NASA Astrophysics Data System (ADS)
Pohle, Rico; Benton, Owen; Jaubert, L. D. C.
2016-07-01
Frustration is often a key ingredient for reentrance mechanisms. Here we study the frustrated anisotropic shuriken Ising model, where it is possible to extend the notion of reentrance between disordered phases, i.e., in absence of phase transitions. By tuning the anisotropy of the lattice, we open a window in the phase diagram where magnetic disorder prevails down to zero temperature, in a classical analogy with a quantum critical point. In this region, the competition between multiple disordered ground states gives rise to a double crossover where both the low- and high-temperature regimes are less correlated than the intervening classical spin liquid. This reentrance of disorder is characterized by an entropy plateau and a multistep Curie law crossover. Our theory is developed based on Monte Carlo simulations, analytical Husimi-tree calculations and an exact decoration-iteration transformation. Its relevance to experiments, in particular, artificial lattices, is discussed.
Modulated phases and chaotic behavior in a spin-1 Ising model with competing interactions
NASA Astrophysics Data System (ADS)
Tomé, Tânia; Salinas, S. R.
1989-02-01
We formulate the Blume-Capel spin-1 Ising model, with competing first- and second-neighbor interactions along the branches of a Cayley tree, in the infinite-coordination limit, as a discrete two-dimensional nonlinear mapping problem. The phase diagram displays multicritical points and many modulated phases. Mean-field calculations for the analogous model on a cubic lattice give the same qualitative results. We take advantage of the simplicity of the mapping to show the existence of complete devil's staircases, at low temperatures T, with increasing values of the Hausdorff dimensionality DF with T. We show that there are regions of the phase diagram associated with positive values of the Lyapunov exponents of the mapping, and we give strong numerical evidence to support the existence of a strange attractor with a Lyapunov dimension Dλ>1. We also find a route to chaos, according to the scenario of Feigenbaum, with a reasonable estimate of the exponent δ.
Phase Transitions for Quantum Markov Chains Associated with Ising Type Models on a Cayley Tree
NASA Astrophysics Data System (ADS)
Mukhamedov, Farrukh; Barhoumi, Abdessatar; Souissi, Abdessatar
2016-05-01
The main aim of the present paper is to prove the existence of a phase transition in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind of models do not have one-dimensional analogous, i.e. the considered model persists only on trees. In this paper, we provide a more general construction of forward QMC. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Our main result states the existence of a phase transition for the Ising model with competing interactions on a Cayley tree of order two. By the phase transition we mean the existence of two distinct QMC which are not quasi-equivalent and their supports do not overlap. We also study some algebraic property of the disordered phase of the model, which is a new phenomena even in a classical setting.
Neutron diffraction study on the two-dimensional Ising system KEr(MoO{sub 4}){sub 2}
Mat'as, Slavomir; Dudzik, Esther; Feyerherm, Ralf; Gerischer, Sebastian; Klemke, Sebastian; Prokes, Karel; Orendacova, Alzbeta
2010-11-01
The magnetic properties of the two-dimensional Ising antiferromagnet KEr(MoO{sub 4}){sub 2} have been investigated below and above transition temperature T{sub N}{approx}0.95 K in zero field and in fields up to 6.5 T by means of elastic neutron-diffraction, heat-capacity, and magnetization measurements. The low-temperature signal recorded at 0.34 K by neutron diffraction is explained within a noncollinear magnetic structure model. However, additional contribution is also present when applying the external magnetic field along the c axis even at temperatures well above the magnetic transition temperature T{sub N}. Various explanations are discussed.
Amoruso, C.; Moore, M. A.; Hartmann, A. K.; Hastings, M. B.
2006-12-31
We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain wall distributions in one geometry can be related to that in a second geometry by a conformal transformation. We also present direct evidence that the domain walls are stochastic Loewner (SLE) processes with {kappa}{approx_equal}2.1. An argument is given that their fractal dimension d{sub f} is related to their interface energy exponent {theta} by d{sub f}-1=3/[4(3+{theta})], which is consistent with the commonly quoted values d{sub f}{approx_equal}1.27 and {theta}{approx_equal}-0.28.
A simulation of the mixed spin 3-spin 3/2 ferrimagnetic Ising model
NASA Astrophysics Data System (ADS)
Özkan, Aycan
2016-01-01
The mixed spin 3-spin 3/2 ferrimagnetic Ising model was simulated using cooling algorithm on cellular automaton (CA). The simulations were carried out in the intervals -4 ≤ DA/J ≤ 8 and -4 ≤ DB/J ≤ 8 for the square lattices with periodic boundary conditions. The ground-state phase diagram of the model has different types of ferrimagnetic phases. Although only the antiferromagnetic nearest-neighbor interaction was contained in the Hamiltonian, the compensation points emerged through DA/J = 2 at kT/J = 0. The values of the critical exponents (ν, α , β and γ) were estimated within the framework of the finite-size scaling theory and power-law relations for the selected DA/J values (-2, 0, 1, 2, and 4). The estimated critical exponent values were in good agreement with the universal values of the two-dimensional Ising model (ν = 1, α = α‧ = 0, β = 0.125, β‧ = 0.875 and γ = γ‧ = 1.75).
Differential geometry of the space of Ising models
NASA Astrophysics Data System (ADS)
Machta, Benjamin; Chachra, Ricky; Transtrum, Mark; Sethna, James
2012-02-01
We use information geometry to understand the emergence of simple effective theories, using an Ising model perturbed with terms coupling non-nearest-neighbor spins as an example. The Fisher information is a natural metric of distinguishability for a parameterized space of probability distributions, applicable to models in statistical physics. Near critical points both the metric components (four-point susceptibilities) and the scalar curvature diverge with corresponding critical exponents. However, connections to Renormalization Group (RG) ideas have remained elusive. Here, rather than looking at RG flows of parameters, we consider the reparameterization-invariant flow of the manifold itself. To do this we numerically calculate the metric in the original parameters, taking care to use only information available after coarse-graining. We show that under coarse-graining the metric contracts very anisotropically, leading to a ``sloppy'' spectrum with the metric's Eigenvalues spanning many orders of magnitude. Our results give a qualitative explanation for the success of simple models: most directions in parameter space become fundamentally indistinguishable after coarse-graining.
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.
Universal Finite Size Corrections and the Central Charge in Non-solvable Ising Models
NASA Astrophysics Data System (ADS)
Giuliani, Alessandro; Mastropietro, Vieri
2013-11-01
We investigate a non-solvable two-dimensional ferromagnetic Ising model with nearest neighbor plus weak finite range interactions of strength λ. We rigorously establish one of the predictions of Conformal Field Theory (CFT), namely the fact that at the critical temperature the finite size corrections to the free energy are universal, in the sense that they are exactly independent of the interaction. The corresponding central charge, defined in terms of the coefficient of the first subleading term to the free energy, as proposed by Affleck and Blote-Cardy-Nightingale, is constant and equal to 1/2 for all and λ 0 a small but finite convergence radius. This is one of the very few cases where the predictions of CFT can be rigorously verified starting from a microscopic non solvable statistical model. The proof uses a combination of rigorous renormalization group methods with a novel partition function inequality, valid for ferromagnetic interactions.
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.
Form factor expansions in the 2D Ising model and Painlevé VI
NASA Astrophysics Data System (ADS)
Mangazeev, Vladimir V.; Guttmann, Anthony J.
2010-10-01
We derive a Toda-type recurrence relation, in both high- and low-temperature regimes, for the λ-extended diagonal correlation functions C(N,N;λ) of the two-dimensional Ising model, using an earlier connection between diagonal form factor expansions and tau-functions within Painlevé VI (PVI) theory, originally discovered by Jimbo and Miwa. This greatly simplifies the calculation of the diagonal correlation functions, particularly their λ-extended counterparts. We also conjecture a closed form expression for the simplest off-diagonal case C(0,1;λ) where a connection to PVI theory is not known. Combined with the results for diagonal correlations these give all the initial conditions required for the λ-extended version of quadratic difference equations for the correlation functions discovered by McCoy, Perk and Wu. The results obtained here should provide a further potential algorithmic improvement in the λ-extended case, and facilitate other developments.
Optimal control in nonequilibrium systems: Dynamic Riemannian geometry of the Ising model
NASA Astrophysics Data System (ADS)
Rotskoff, Grant M.; Crooks, Gavin E.
2015-12-01
A general understanding of optimal control in nonequilibrium systems would illuminate the operational principles of biological and artificial nanoscale machines. Recent work has shown that a system driven out of equilibrium by a linear response protocol is endowed with a Riemannian metric related to generalized susceptibilities, and that geodesics on this manifold are the nonequilibrium control protocols with the lowest achievable dissipation. While this elegant mathematical framework has inspired numerous studies of exactly solvable systems, no description of the thermodynamic geometry yet exists when the metric cannot be derived analytically. Herein, we numerically construct the dynamic metric of the two-dimensional Ising model in order to study optimal protocols for reversing the net magnetization.
±J Ising model on homogeneous Archimedean lattices
NASA Astrophysics Data System (ADS)
Valdés, J. F.; Lebrecht, W.; Vogel, E. E.
2012-04-01
We tackle the problem of finding analytical expressions describing the ground state properties of homogeneous Archimedean lattices over which a generalized Edwards-Anderson model (±J Ising model) is defined. A local frustration analysis is performed based on representative cells for square lattices, triangular lattices and honeycomb lattices. The concentration of ferromagnetic (F) bonds x is used as the independent variable in the analysis (1-x is the concentration for antiferromagnetic (A) bonds), where x spans the range [0.0,1.0]. The presence of A bonds brings frustration, whose clear manifestation is when bonds around the minimum possible circuit of bonds (plaquette) cannot be simultaneously satisfied. The distribution of curved (frustrated) plaquettes within the representative cell is determinant for the evaluation of the parameters of interest such as average frustration segment, energy per bond, and fractional content of unfrustrated bonds. Two methods are developed to cope with this analysis: one based on the direct probability of a plaquette being curved; the other one is based on the consideration of the different ways bonds contribute to the particular plaquette configuration. Exact numerical simulations on a large number of randomly generated samples allow to validate previously described theoretical analysis. It is found that the second method presents slight advantages over the first one. However, both methods give an excellent description for most of the range for x. The small deviations at specific intervals of x for each lattice have to do with the self-imposed limitations of both methods due to practical reasons. A particular discussion for the point x=0.5 for each one of the lattices also shines light on the general trends of the properties described here.
Hyperinflation in the Ising model on quasiperiodic chains
NASA Astrophysics Data System (ADS)
Odagaki, T.
1990-02-01
Using a hyperinflation rule, the free energy of the two component Ising system on a chain with an arbitrary quasiperiodic order is shown to be given by an average of the free energy of each component, in agreement with the result obtained by the transfer matrix formalism.
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.
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.
Exact algorithm for sampling the two-dimensional Ising spin glass.
Thomas, Creighton K; Middleton, A Alan
2009-10-01
A sampling algorithm is presented that generates spin-glass configurations of the two-dimensional Edwards-Anderson Ising spin glass at finite temperature with probabilities proportional to their Boltzmann weights. Such an algorithm overcomes the slow dynamics of direct simulation and can be used to study long-range correlation functions and coarse-grained dynamics. The algorithm uses a correspondence between spin configurations on a regular lattice and dimer (edge) coverings of a related graph: Wilson's algorithm [D. B. Wilson, Proceedings of the Eighth Symposium on Discrete Algorithms (SIAM, Philadelphia, 1997), p 258] for sampling dimer coverings on a planar lattice is adapted to generate samplings for the dimer problem corresponding to both planar and toroidal spin-glass samples. This algorithm is recursive: it computes probabilities for spins along a "separator" that divides the sample in half. Given the spins on the separator, sample configurations for the two separated halves are generated by further division and assignment. The algorithm is simplified by using Pfaffian elimination rather than Gaussian elimination for sampling dimer configurations. For n spins and given floating point precision, the algorithm has an asymptotic run-time of O(n(3/2)); it is found that the required precision scales as inverse temperature and grows only slowly with system size. Sample applications and benchmarking results are presented for samples of size up to n=128(2), with fixed and periodic boundary conditions. PMID:19905483
NASA Astrophysics Data System (ADS)
Fytas, Nikolaos G.; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas
2016-06-01
By performing a high-statistics simulation of the D =4 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to describe the transition.
Exact solution of the spin-1/2 Ising model on the Shastry Sutherland (orthogonal-dimer) lattice
NASA Astrophysics Data System (ADS)
Strečka, Jozef
2006-01-01
A star-triangle mapping transformation is used to establish an exact correspondence between the spin-1/2 Ising model on the Shastry Sutherland (orthogonal-dimer) lattice and respectively, the spin-1/2 Ising model on a bathroom tile (4 8) lattice. Exact results for the critical temperature and spontaneous magnetization are obtained and compared with corresponding results on the regular Ising lattices.
NASA Astrophysics Data System (ADS)
Lopes Cardozo, David; Holdsworth, Peter C. W.
2016-04-01
The magnetization probability density in d = 2 and 3 dimensional Ising models in slab geometry of volume L\\paralleld-1× {{L}\\bot} is computed through Monte-Carlo simulation at the critical temperature and zero magnetic field. The finite-size scaling of this distribution and its dependence on the system aspect-ratio ρ =\\frac{{{L}\\bot}}{{{L}\\parallel}} and boundary conditions are discussed. In the limiting case ρ \\to 0 of a macroscopically large slab ({{L}\\parallel}\\gg {{L}\\bot} ) the distribution is found to scale as a Gaussian function for all tested system sizes and boundary conditions.
Physics and financial economics (1776-2014): puzzles, Ising and agent-based models.
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. PMID:24875470
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.
Canonical vs. micro-canonical sampling methods in a 2D Ising model
Kepner, J.
1990-12-01
Canonical and micro-canonical Monte Carlo algorithms were implemented on a 2D Ising model. Expressions for the internal energy, U, inverse temperature, Z, and specific heat, C, are given. These quantities were calculated over a range of temperature, lattice sizes, and time steps. Both algorithms accurately simulate the Ising model. To obtain greater than three decimal accuracy from the micro-canonical method requires that the more complicated expression for Z be used. The overall difference between the algorithms is small. The physics of the problem under study should be the deciding factor in determining which algorithm to use. 13 refs., 6 figs., 2 tabs.
Self-Organizing Two-Temperature Ising Model Describing Human Segregation
NASA Astrophysics Data System (ADS)
Ódor, Géza
A two-temperature Ising-Schelling model is introduced and studied for describing human segregation. The self-organized Ising model with Glauber kinetics simulated by Müller et al. exhibits a phase transition between segregated and mixed phases mimicking the change of tolerance (local temperature) of individuals. The effect of external noise is considered here as a second temperature added to the decision of individuals who consider a change of accommodation. A numerical evidence is presented for a discontinuous phase transition of the magnetization.
Relations between short-range and long-range Ising models
NASA Astrophysics Data System (ADS)
Angelini, Maria Chiara; Parisi, Giorgio; Ricci-Tersenghi, Federico
2014-06-01
We perform a numerical study of the long-range (LR) ferromagnetic Ising model with power law decaying interactions (J ∝r-d-σ) on both a one-dimensional chain (d =1) and a square lattice (d =2). We use advanced cluster algorithms to avoid the critical slowing down. We first check the validity of the relation connecting the critical behavior of the LR model with parameters (d,σ) to that of a short-range (SR) model in an equivalent dimension D. We then study the critical behavior of the d =2 LR model close to the lower critical σ, uncovering that the spatial correlation function decays with two different power laws: The effect of the subdominant power law is much stronger than finite-size effects and actually makes the estimate of critical exponents very subtle. By including this subdominant power law, the numerical data are consistent with the standard renormalization group (RG) prediction by Sak [Phys. Rev. B 8, 281 (1973), 10.1103/PhysRevB.8.281], thus making not necessary (and unlikely, according to Occam's razor) the recent proposal by Picco [arXiv:1207.1018] of having a new set of RG fixed points in addition to the mean-field one and the SR one.
Relations between short-range and long-range Ising models.
Angelini, Maria Chiara; Parisi, Giorgio; Ricci-Tersenghi, Federico
2014-06-01
We perform a numerical study of the long-range (LR) ferromagnetic Ising model with power law decaying interactions (J∝r{-d-σ}) on both a one-dimensional chain (d=1) and a square lattice (d=2). We use advanced cluster algorithms to avoid the critical slowing down. We first check the validity of the relation connecting the critical behavior of the LR model with parameters (d,σ) to that of a short-range (SR) model in an equivalent dimension D. We then study the critical behavior of the d=2 LR model close to the lower critical σ, uncovering that the spatial correlation function decays with two different power laws: The effect of the subdominant power law is much stronger than finite-size effects and actually makes the estimate of critical exponents very subtle. By including this subdominant power law, the numerical data are consistent with the standard renormalization group (RG) prediction by Sak [Phys. Rev. B 8, 281 (1973)], thus making not necessary (and unlikely, according to Occam's razor) the recent proposal by Picco [arXiv:1207.1018] of having a new set of RG fixed points in addition to the mean-field one and the SR one. PMID:25019738
NASA Astrophysics Data System (ADS)
Hasenbusch, Martin
2010-09-01
We study the thermodynamic Casimir force for films in the three-dimensional Ising universality class with symmetry-breaking boundary conditions. To this end we simulate the improved Blume-Capel model on the simple cubic lattice. We study the two cases ++ , where all spins at the boundary are fixed to +1 and +- , where the spins at one boundary are fixed to +1 while those at the other boundary are fixed to -1 . An important issue in analyzing Monte Carlo and experimental data are corrections to scaling. Since we simulate an improved model, leading corrections to scaling, which are proportional to L0-ω , where L0 is the thickness of the film and ω≈0.8 , can be ignored. This allows us to focus on corrections to scaling that are caused by the boundary conditions. The analysis of our data shows that these corrections can be accounted for by an effective thickness L0,eff=L0+Ls . Studying the correlation length of the films, the energy per area, the magnetization profile, and the thermodynamic Casimir force at the bulk critical point we find Ls=1.9(1) for our model and the boundary conditions discussed here. Using this result for Ls we find a nice collapse of the finite-size scaling curves obtained for the thicknesses L0=8.5 , 16.5, and 32.5 for the full range of temperatures that we consider. We compare our results for the finite-size scaling functions θ++ and θ+- of the thermodynamic Casimir force with those obtained in a previous Monte Carlo study, by the de Gennes-Fisher local-functional method, field theoretic methods, and an experiment with a classical binary liquid mixture.
The Finite-Size Scaling Study of the Ising Model for the Fractals
NASA Astrophysics Data System (ADS)
Merdan, Z.; Bayirli, M.; Günen, A.; Bülbül, M.
2016-04-01
The fractals are obtained by using the model of diffusion-limited aggregation (DLA) for 40 ≤ L ≤ 240. The two-dimensional Ising model is simulated on the Creutz cellular automaton for 40 ≤ L ≤ 240. The critical exponents and the fractal dimensions are computed to be β = 0.124(8), γ = 1.747(10), α = 0.081(21), δ = 14.994(11), η = 0.178(10), ν = 0.960(23) and df^{β } =1.876(8), df^{γ } =3.747(10), df^{α } =2.081(68), df^{δ } =1.940(22), df^{η } =2.178(10), df^{ν } =2.960(22), which are consistent with the theoretical values of β = 0.125, γ = 1.75, α = 0, δ = 15, η = 0.25, ν = 1 and df^{β } =1.875, df^{γ } =3.75, df^{α } =2, df^{δ } =1.933, df^{η } =2.25, df^{ν } =3.
Spontaneous magnetization of the Ising model on the union jack and 4-6 lattices
NASA Astrophysics Data System (ADS)
Lin, K. Y.; Wang, S. C.
1988-03-01
Spontaneous magnetization of the Ising model on the anisotropic Union Jack and 4-6 lattices are derived exactly. The conjecture by Lin and Wang is confirmed. Our result is a generalization of the recent work on the isotropic Union Jack lattice by Choy and Baxter.
Spontaneous magnetization of the Ising model on a 4-8 lattice
NASA Astrophysics Data System (ADS)
Lin, K. Y.
1988-03-01
Spontaneous magnetization of the Ising model on a 4-8 lattice is derived. The result agrees with the conjecture of Lin, Kao and Chen. Our derivation is closely related to the recent work of Choy and Baxter on the isotropic Union Jack lattice.
ADDENDUM: Addendum to `On the singularity structure of the 2D Ising model susceptibility'
NASA Astrophysics Data System (ADS)
Nickel, Bernie
2000-03-01
A remarkable product formula first derived by Palmer and Tracy (1981 Adv. Appl. Math. 2 329) for the integrand of the two-dimensional Ising model susceptibility expansion coefficients icons/Journals/Common/chi" ALT="chi" ALIGN="TOP"/> (2n ) for temperatures T less than the critical T c is shown to apply equally for icons/Journals/Common/chi" ALT="chi" ALIGN="TOP"/> (2n +1) for T >T c and agrees with formulae derived by Yamada (1984 Prog. Theor. Phys. 71 1416). This new representation simplifies the derivation of the results in the original paper of this title (1999 J. Phys. A: Math. Gen. 32 3889) to the extent that the leading series behaviour and the singularity structure can be deduced almost by inspection. The derivation of series is also simplified and I show, using extended series and knowledge of the singularity structure, that there is now unambiguous evidence for correction to scaling terms in the susceptibility beyond those inferred from a nonlinear scaling field analysis.
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.
Magnetization plateaus and phase diagrams of the Ising model on the Shastry-Sutherland lattice
NASA Astrophysics Data System (ADS)
Deviren, Seyma Akkaya
2015-11-01
The magnetization properties of a two-dimensional spin-1/2 Ising model on the Shastry-Sutherland lattice are studied within the effective-field theory (EFT) with correlations. The thermal behavior of the magnetizations is investigated in order to characterize the nature (the first- or second-order) of the phase transitions as well as to obtain the phase diagrams of the model. The internal energy, specific heat, entropy and free energy of the system are also examined numerically as a function of the temperature in order to confirm the stability of the phase transitions. The applied field dependence of the magnetizations is also examined to find the existence of the magnetization plateaus. For strong enough magnetic fields, several magnetization plateaus are observed, e.g., at 1/9, 1/8, 1/3 and 1/2 of the saturation. The phase diagrams of the model are constructed in two different planes, namely (h/|J|, |J‧|/|J|) and (h/|J|, T/|J|) planes. It was found that the model exhibits first- and second-order phase transitions; hence tricitical point is also observed in additional to the zero-temperature critical point. Moreover the Néel order (N), collinear order (C) and ferromagnetic (F) phases are also found with appropriate values of the system parameters. The reentrant behavior is also obtained whenever model displays two Néel temperatures. These results are compared with some theoretical and experimental works and a good overall agreement has been obtained.
Aspelmeier, T; Wang, Wenlong; Moore, M A; Katzgraber, Helmut G
2016-08-01
The one-dimensional Ising spin-glass model with power-law long-range interactions is a useful proxy model for studying spin glasses in higher space dimensions and for finding the dimension at which the spin-glass state changes from having broken replica symmetry to that of droplet behavior. To this end we have calculated the exponent that describes the difference in free energy between periodic and antiperiodic boundary conditions. Numerical work is done to support some of the assumptions made in the calculations and to determine the behavior of the interface free-energy exponent of the power law of the interactions. Our numerical results for the interface free-energy exponent are badly affected by finite-size problems. PMID:27627255
NASA Astrophysics Data System (ADS)
Aspelmeier, T.; Wang, Wenlong; Moore, M. A.; Katzgraber, Helmut G.
2016-08-01
The one-dimensional Ising spin-glass model with power-law long-range interactions is a useful proxy model for studying spin glasses in higher space dimensions and for finding the dimension at which the spin-glass state changes from having broken replica symmetry to that of droplet behavior. To this end we have calculated the exponent that describes the difference in free energy between periodic and antiperiodic boundary conditions. Numerical work is done to support some of the assumptions made in the calculations and to determine the behavior of the interface free-energy exponent of the power law of the interactions. Our numerical results for the interface free-energy exponent are badly affected by finite-size problems.
Graphical Representations for Ising and Potts Models in General External Fields
NASA Astrophysics Data System (ADS)
Cioletti, Leandro; Vila, Roberto
2016-01-01
This work is concerned with the theory of graphical representation for the Ising and Potts models over general lattices with non-translation invariant external field. We explicitly describe in terms of the random-cluster representation the distribution function and, consequently, the expected value of a single spin for the Ising and q-state Potts models with general external fields. We also consider the Gibbs states for the Edwards-Sokal representation of the Potts model with non-translation invariant magnetic field and prove a version of the FKG inequality for the so called general random-cluster model (GRC model) with free and wired boundary conditions in the non-translation invariant case. Adding the amenability hypothesis on the lattice, we obtain the uniqueness of the infinite connected component and the almost sure quasilocality of the Gibbs measures for the GRC model with such general magnetic fields. As a final application of the theory developed, we show the uniqueness of the Gibbs measures for the ferromagnetic Ising model with a positive power-law decay magnetic field with small enough power, as conjectured in Bissacot et al. (Commun Math Phys 337: 41-53, 2015).
A universal form of slow dynamics in zero-temperature random-field Ising model
NASA Astrophysics Data System (ADS)
Ohta, H.; Sasa, S.
2010-04-01
The zero-temperature Glauber dynamics of the random-field Ising model describes various ubiquitous phenomena such as avalanches, hysteresis, and related critical phenomena. Here, for a model on a random graph with a special initial condition, we derive exactly an evolution equation for an order parameter. Through a bifurcation analysis of the obtained equation, we reveal a new class of cooperative slow dynamics with the determination of critical exponents.
NASA Astrophysics Data System (ADS)
Decelle, Aurélien; Ricci-Tersenghi, Federico
2014-02-01
In this Letter we propose a new method to infer the topology of the interaction network in pairwise models with Ising variables. By using the pseudolikelihood method (PLM) at high temperature, it is generally possible to distinguish between zero and nonzero couplings because a clear gap separate the two groups. However at lower temperatures the PLM is much less effective and the result depends on subjective choices, such as the value of the ℓ1 regularizer and that of the threshold to separate nonzero couplings from null ones. We introduce a decimation procedure based on the PLM that recursively sets to zero the less significant couplings, until the variation of the pseudolikelihood signals that relevant couplings are being removed. The new method is fully automated and does not require any subjective choice by the user. Numerical tests have been performed on a wide class of Ising models, having different topologies (from random graphs to finite dimensional lattices) and different couplings (both diluted ferromagnets in a field and spin glasses). These numerical results show that the new algorithm performs better than standard PLM.
Universal critical behavior of the two-dimensional Ising spin glass
NASA Astrophysics Data System (ADS)
Fernandez, L. A.; Marinari, E.; Martin-Mayor, V.; Parisi, G.; Ruiz-Lorenzo, J. J.
2016-07-01
We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated temperature dependency of the scaling fields is identified as the major obstacle that has impeded a complete analysis. Once temperature is relinquished in favor of the correlation length as the basic variable, we obtain a reliable estimation of the anomalous dimension and of the thermal critical exponent. Universality among binary and Gaussian couplings is confirmed to a high numerical accuracy.
NASA Technical Reports Server (NTRS)
Spjeldvik, W. N.; Fritz, T. A.
1981-01-01
A description of energetic ion and electron behavior in the geomagnetic plasma sheet boundary layer is presented based on observations made by the medium-energy particle experiment on board ISEE 1. Three-dimensional observations of ions of energies 24-2081 keV and electrons of energies 22.5-1200 keV were obtained by the NOAA/WAPS instrument near the center of the magnetotail at a distance of approximately 15 earth radii. Large-scale motions of plasma sheet energetic particles are observed as an apparent result of a series of magnetospheric disturbances (substorms), which are characterized by substantial contractions and expansions. Ion flow velocity in a distinct boundary layer in energetic ions has been found to be in the earthward direction in each of the five ISEE 1 boundary crossings. Boundary layer motion during one of these crossings is interpreted as large-amplitude boundary waves with periodicities of a few minutes superimposed on the general plasma sheet behavior associated with the substorm process.
Morris, C M; Valdés Aguilar, R; Ghosh, A; Koohpayeh, S M; Krizan, J; Cava, R J; Tchernyshyov, O; McQueen, T M; Armitage, N P
2014-04-01
Kink bound states in the one-dimensional ferromagnetic Ising chain compound CoNb2O6 have been studied using high-resolution time-domain terahertz spectroscopy in zero applied magnetic field. When magnetic order develops at low temperature, nine bound states of kinks become visible. Their energies can be modeled exceedingly well by the Airy function solutions to a 1D Schrödinger equation with a linear confining potential. This sequence of bound states terminates at a threshold energy near 2 times the energy of the lowest bound state. Above this energy scale we observe a broad feature consistent with the onset of the two particle continuum. At energies just below this threshold we observe a prominent excitation that we interpret as a novel bound state of bound states--two pairs of kinks on neighboring chains. PMID:24745454
NASA Astrophysics Data System (ADS)
Morris, C. M.; Valdés Aguilar, R.; Ghosh, A.; Koohpayeh, S. M.; Krizan, J.; Cava, R. J.; Tchernyshyov, O.; McQueen, T. M.; Armitage, N. P.
2014-04-01
Kink bound states in the one-dimensional ferromagnetic Ising chain compound CoNb2O6 have been studied using high-resolution time-domain terahertz spectroscopy in zero applied magnetic field. When magnetic order develops at low temperature, nine bound states of kinks become visible. Their energies can be modeled exceedingly well by the Airy function solutions to a 1D Schrödinger equation with a linear confining potential. This sequence of bound states terminates at a threshold energy near 2 times the energy of the lowest bound state. Above this energy scale we observe a broad feature consistent with the onset of the two particle continuum. At energies just below this threshold we observe a prominent excitation that we interpret as a novel bound state of bound states—two pairs of kinks on neighboring chains.
Magnetic and Ising quantum phase transitions in a model for isoelectronically tuned iron pnictides
NASA Astrophysics Data System (ADS)
Wu, Jianda; Si, Qimiao; Abrahams, Elihu
2016-03-01
Considerations of the observed bad-metal behavior in Fe-based superconductors led to an early proposal for quantum criticality induced by isoelectronic P for As doping in iron arsenides, which has since been experimentally confirmed. We study here an effective model for the isoelectronically tuned pnictides using a large-N approach. The model contains antiferromagnetic and Ising-nematic order parameters appropriate for J1-J2 exchange-coupled local moments on an Fe square lattice, and a damping caused by coupling to itinerant electrons. The zero-temperature magnetic and Ising transitions are concurrent and essentially continuous. The order-parameter jumps are very small, and are further reduced by the interplane coupling; consequently, quantum criticality occurs over a wide dynamical range. Our results reconcile recent seemingly contradictory experimental observations concerning the quantum phase transition in the P-doped iron arsenides.
Ising-like phase transition of an n-component Eulerian face-cubic model
NASA Astrophysics Data System (ADS)
Ding, Chengxiang; Guo, Wenan; Deng, Youjin
2013-11-01
By means of Monte Carlo simulations and a finite-size scaling analysis, we find a critical line of an n-component Eulerian face-cubic model on the square lattice and the simple cubic lattice in the region v>1, where v is the bond weight. The phase transition belongs to the Ising universality class independent of n. The critical properties of the phase transition can also be captured by the percolation of the complement of the Eulerian graph.
Smeared quantum phase transition in the dissipative random quantum Ising model
NASA Astrophysics Data System (ADS)
Vojta, Thomas; Hoyos, José A.
2010-01-01
We investigate the quantum phase transition in the random transverse-field Ising model under the influence of Ohmic dissipation. To this end, we numerically implement a strong-disorder renormalization-group scheme. We find that Ohmic dissipation destroys the quantum critical point and the associated quantum Griffiths phase by smearing. Our results quantitatively confirm a recent theory [J.A. Hoyos, T. Vojta, Phys. Rev. Lett. 100 (2008) 240601] of smeared quantum phase transitions.
Form factors in the Bullough-Dodd-related models: The Ising model in a magnetic field
NASA Astrophysics Data System (ADS)
Alekseev, O. V.
2012-11-01
We consider a certain modification of the free-field representation of the form factors in the Bullough-Dodd model. The two-particle minimal form factors are eliminated from the construction. We consequently obtain a convenient representation for the multiparticle form factors, establish recurrence relations between them, and study their properties. We use the proposed construction to obtain the free-field representation of form factors for the lightest particles in the Φ 1,2 -perturbed minimal models. As an important example, we consider the Ising model in a magnetic field. We verify that the results obtained in the framework of the proposed free-field representation agree with the corresponding results obtained by solving the bootstrap equations.
Form factors in the Bullough-Dodd related models: The Ising model in a magnetic field
NASA Astrophysics Data System (ADS)
Alekseev, O. V.
2012-04-01
A particular modification of the free-field representation of the form factors in the Bullough-Dodd model is considered. The two-particles minimal form factors are excluded from the construction. As a consequence, a convenient representation for the multiparticle form factors has been obtained, recurrence relations between them have been established, and their properties have been studied. The proposed construction is used to obtain the free-field representation of the lightest particles form factors in the Φ1, 2 perturbed minimal models. The Ising model in a magnetic field is considered as a significant example. The results obtained in the framework of the proposed free-field representation are in agreement with the corresponding results obtained by solving the bootstrap equations.
Inference of the sparse kinetic Ising model using the decimation method.
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)] 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 ℓ(1)-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 ℓ(1)-optimization-based methods. PMID:26066148
Evidence for two-dimensional Ising superconductivity in gated MoS₂.
Lu, J M; Zheliuk, O; Leermakers, I; Yuan, N F Q; Zeitler, U; Law, K T; Ye, J T
2015-12-11
The Zeeman effect, which is usually detrimental to superconductivity, can be strongly protective when an effective Zeeman field from intrinsic spin-orbit coupling locks the spins of Cooper pairs in a direction orthogonal to an external magnetic field. We performed magnetotransport experiments with ionic-gated molybdenum disulfide transistors, in which gating prepared individual superconducting states with different carrier dopings, and measured an in-plane critical field B(c2) far beyond the Pauli paramagnetic limit, consistent with Zeeman-protected superconductivity. The gating-enhanced B(c2) is more than an order of magnitude larger than it is in the bulk superconducting phases, where the effective Zeeman field is weakened by interlayer coupling. Our study provides experimental evidence of an Ising superconductor, in which spins of the pairing electrons are strongly pinned by an effective Zeeman field. PMID:26563134
Evidence for two-dimensional Ising superconductivity in gated MoS2
NASA Astrophysics Data System (ADS)
Lu, J. M.; Zheliuk, O.; Leermakers, I.; Yuan, N. F. Q.; Zeitler, U.; Law, K. T.; Ye, J. T.
2015-12-01
The Zeeman effect, which is usually detrimental to superconductivity, can be strongly protective when an effective Zeeman field from intrinsic spin-orbit coupling locks the spins of Cooper pairs in a direction orthogonal to an external magnetic field. We performed magnetotransport experiments with ionic-gated molybdenum disulfide transistors, in which gating prepared individual superconducting states with different carrier dopings, and measured an in-plane critical field Bc2 far beyond the Pauli paramagnetic limit, consistent with Zeeman-protected superconductivity. The gating-enhanced Bc2 is more than an order of magnitude larger than it is in the bulk superconducting phases, where the effective Zeeman field is weakened by interlayer coupling. Our study provides experimental evidence of an Ising superconductor, in which spins of the pairing electrons are strongly pinned by an effective Zeeman field.
Ising spin network states for loop quantum gravity: a toy model for phase transitions
NASA Astrophysics Data System (ADS)
Feller, Alexandre; Livine, Etera R.
2016-03-01
Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should emerge entirely from the correlations between the gravity fluctuations. In the context of loop quantum gravity, quantum states of geometry are defined as spin networks. These are graphs decorated with spin and intertwiners, which represent quantized excitations of areas and volumes of the space geometry. Here, we develop the condensed-matter point of view on extracting the physical and geometrical information from spin network states: we introduce new Ising spin network states, both in 2d on a square lattice and in 3d on a hexagonal lattice, whose correlations map onto the usual Ising model in statistical physics. We construct these states from the basic holonomy operators of loop gravity and derive a set of local Hamiltonian constraints that entirely characterize our states. We discuss their phase diagram and show how the distance can be reconstructed from the correlations in the various phases. Finally, we propose generalizations of these Ising states, which open the perspective to study the coarse-graining and dynamics of spin network states using well-known condensed-matter techniques and results.
Phase transition of p-adic Ising λ-model
Dogan, Mutlay; Akın, Hasan; Mukhamedov, Farrukh
2015-09-18
We consider an interaction of the nearest-neighbors and next nearest-neighbors for the mixed type p-adic λ-model with spin values (−1, +1) on a Cayley tree of order two. In the previous work we have proved the existence of the p-adic Gibbs measure for the model. In this work we have proved the existence of the phase transition occurs for the model.
Ising type models applied to Geophysics and high frequency market data
NASA Astrophysics Data System (ADS)
Mariani, M. C.; Bezdek, P.; Serpa, L.; Florescu, I.
2011-11-01
The classical Ising model was used to re-create the ferromagnetic phenomenon in statistical mechanics. The model describes the behavior of atoms in a lattice. Each atom may interact only with its neighbors, and has two states called spins. When the atoms polarize their spins, the resulting material exhibits a net magnetization. A similar model has been used before in financial math: the spins correspond to the buy/sell position of a trader and the polarization is equivalent with all the traders in the market wanting to sell. This leads to a market crash. In this work, we present extensions and applications to geophysics and high frequency market data.
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…
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.
Monte Carlo Simulations of inter- and intra-grain spin structure of Ising and Heisenberg models
NASA Astrophysics Data System (ADS)
Leblanc, Martin
In order to keep supplying computer hard disk drives with more and more storage space, it is essential to have smaller bits. With smaller bits, superparamagnetism, the spontaneous flipping of the magnetic moments in a bit caused by thermal fluctuations, becomes increasingly important and impacts the stability of stored data. Recording media is composed of magnetic grains (usually made of CoCrPt alloys) roughly 10 nm in size from which bits are composed. Most modeling efforts that study magnetic recording media treat the grains as weakly interacting uniformly magnetized objects. In this work, the spin structure internal to a grain is examined along with the impact of varying the relative strengths of intrar-grain and inter-grain exchange interactions. The interplay between these two effects needs to be examined for a greater understanding of superparamagnetism as well as for the applications of the proposed Heat Assisted Magnetic Recording (HAMR) technology where thermal fluctuations facilitate head-field induced bit reversal in high anisotropy media. Simulations using the Monte Carlo method (with cluster-flipping algorithms) are performed on a 2D single-layer and multilayer Ising model with a strong intrar-grain exchange interaction J as well as a weak inter-grain exchange J'. A strong deviation from traditional behavior is found when J'/J is significant. M-H hysteresis loops are also calculated and the coercivity, H c is estimated. A large value represents a strong resilience to the superparamagnetic effect. It is found that taking into account the internal degrees of freedom has a significant effect on Hce. As the Ising model serves only as an approximation, preliminary simulations are also reported on a more realistic Heisenberg model with uniaxial anisotropy. Key Words: Ising model, Heisenberg model, Monte Carlo Simulation
Ovchinnikov, O. S.; Jesse, S.; Kalinin, S. V.; Bintacchit, P.; Trolier-McKinstry, S.
2009-10-09
An approach for the direct identification of disorder type and strength in physical systems based on recognition analysis of hysteresis loop shape is developed. A large number of theoretical examples uniformly distributed in the parameter space of the system is generated and is decorrelated using principal component analysis (PCA). The PCA components are used to train a feed-forward neural network using the model parameters as targets. The trained network is used to analyze hysteresis loops for the investigated system. The approach is demonstrated using a 2D random-bond-random-field Ising model, and polarization switching in polycrystalline ferroelectric capacitors.
Ultrafast vectorized multispin coding algorithm for the Monte Carlo simulation of the 3D Ising model
NASA Astrophysics Data System (ADS)
Wansleben, Stephan
1987-02-01
A new Monte Carlo algorithm for the 3D Ising model and its implementation on a CDC CYBER 205 is presented. This approach is applicable to lattices with sizes between 3·3·3 and 192·192·192 with periodic boundary conditions, and is adjustable to various kinetic models. It simulates a canonical ensemble at given temperature generating a new random number for each spin flip. For the Metropolis transition probability the speed is 27 ns per updates on a two-pipe CDC Cyber 205 with 2 million words physical memory, i.e. 1.35 times the cycle time per update or 38 million updates per second.
Geometrical aspects of critical Ising configurations in two dimensions
NASA Astrophysics Data System (ADS)
Blöte, H. W. J.; Knops, Y. M. M.; Nienhuis, B.
1992-06-01
We present a physical interpretation of a number of exotic exponents of the two-dimensional Ising model, i.e., exponents that do have a conformal classification, but outside the unitary grid. They describe the scaling behavior of geometric properties of Ising and random clusters. For instance, the probability that two spins at a distance r lie on the perimeter of the same Ising cluster decays as r-5/4 at criticality. These results are obtained via mappings on the Coulomb gas. A part of the Coulomb gas scenario is verified by means of finite-size scaling of transfer-matrix results.
LETTER TO THE EDITOR: Frustration in Ising-type spin models on the pyrochlore lattice
NASA Astrophysics Data System (ADS)
Bramwell, S. T.; Harris, M. J.
1998-04-01
We compare the behaviour of ferromagnetic and antiferromagnetic Ising-type spin models on the cubic pyrochlore lattice. With simple `up - down' Ising spins, the antiferromagnet is highly frustrated and the ferromagnet is not. However, such spin symmetry cannot be realized on the pyrochlore lattice, since it requires a unique symmetry axis, which is incompatible with the cubic symmetry. The only two-state spin symmetry which is compatible is that with four local 0953-8984/10/14/002/img5 anisotropy axes, which direct the spins to point in or out of the tetrahedral plaquettes of the pyrochlore lattice. We show how the local `in - out' magnetic anisotropy reverses the roles of the ferro- and antiferromagnetic exchange couplings with regard to frustration, such that the ferromagnet is highly frustrated and the antiferromagnet is not. The in - out ferromagnet is a magnetic analogue of the ice model, which we have termed the `spin ice model'. It is realized in the material 0953-8984/10/14/002/img6. The up - down antiferromagnet is also an analogue of the ice model, albeit a less direct one, as originally shown by Anderson. Combining these results shows that the up - down spin models map onto the in - out spin models with the opposite sign of the exchange coupling. We present Monte Carlo simulations of the susceptibility for each model, and discuss their relevance to experimental systems.
Onsager and Kaufman's Calculation of the Spontaneous Magnetization of the Ising Model
NASA Astrophysics Data System (ADS)
Baxter, R. J.
2011-11-01
Lars Onsager announced in 1949 that he and Bruria Kaufman had proved a simple formula for the spontaneous magnetization of the square-lattice Ising model, but did not publish their derivation. It was three years later when C.N. Yang published a derivation in Physical Review. In 1971 Onsager gave some clues to his and Kaufman's method, and there are copies of their correspondence in 1950 now available on the Web and elsewhere. Here we review how the calculation appears to have developed, and add a copy of a draft paper, almost certainly by Onsager and Kaufman, that obtains the result.
Condensation of helium in aerogel and athermal dynamics of the random-field Ising model.
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. PMID:25192103
Exact results for the site-dilute antiferromagnetic Ising model on finite triangular lattices
NASA Astrophysics Data System (ADS)
Farach, H. A.; Creswick, R. J.; Poole, C. P., Jr.
1988-04-01
Exact analytical and numerical results for the site-diluted antiferromagnetic Ising model on the triangular lattice (AFIT) are presented. For infinitesimal dilution the change in the free energy of the system is related to the distribution of local fields, and it is shown that for a frustrated system such as the AFIT, dilution lowers the entropy per spin. For lattices of finite size and dilution the transfer matrix for the partition function is evaluated numerically. The entropy per spin shows a marked minimum near a concentration of spins x=0.70, in some disagreement with earlier transfer-matrix results.
An Ising-like model for monolayer-monolayer coupling in lipid bilayers
NASA Astrophysics Data System (ADS)
Sornbundit, Kan; Modchang, Charin; Nuttavut, Narin; Ngamsaad, Waipot; Triampo, Darapond; Triampo, Wannapong
2013-07-01
We have proposed the Ising bilayer model to study the domain growth dynamics in lipid bilayers. Interactions within and between layers are adopted from recent experimental and theoretical data. We investigate the effects of the mismatch area on the domain coarsening dynamics in both symmetric and asymmetric lipid bilayers. To explore domain coarsening, we used the Monte Carlo (MC) method with a standard Kawasaki dynamics to simulate the systems. The results show that domains on both layers grow following a power-law and that the domains grow slower when the mismatch areas are increased.
The Ising model for changes in word ordering rules in natural languages
NASA Astrophysics Data System (ADS)
Itoh, Yoshiaki; Ueda, Sumie
2004-11-01
The order of ‘noun and adposition’ is an important parameter of word ordering rules in the world’s languages. The seven parameters, ‘adverb and verb’ and others, depend strongly on the ‘noun and adposition’. Japanese as well as Korean, Tamil and several other languages seem to have a stable structure of word ordering rules, while Thai and other languages, which have the opposite word ordering rules to Japanese, are also stable in structure. It seems therefore that each language in the world fluctuates between these two structures like the Ising model for finite lattice.
Supporting Kibble-Zurek Mechanism in Quantum Ising Model through a Trapped Ion
NASA Astrophysics Data System (ADS)
Hu, Changkang; Cui, Jinming; Huang, Yunfeng; Wang, Zhao; Cao, Dongyang; Wang, Jian; Lv, Weimin; Lu, Yong; Luo, Le; Campo, Adolfo; Han, Yongjian; Li, Chuanfeng; Guo, Guangcan
The Kibble-Zurek mechanism is the paradigm to account for the non adiabatic dynamics of a system across a phase transition. Its study in the quantum regime is hindered by the requisite of ground state cooling. We report the experimental quantum simulation of critical dynamics in the transverse-field Ising model by a set of Landau-Zener crossings in pseudo-momentum space, that can be probed with high accuracy using a single trapped ion. Our results support the Kibble-Zurek mechanism in the quantum regime and advance the quantum simulation of critical systems far-away from equilibrium.
The Ising model for prediction of disordered residues from protein sequence alone
NASA Astrophysics Data System (ADS)
Lobanov, Michail Yu; Galzitskaya, Oxana V.
2011-06-01
Intrinsically disordered regions serve as molecular recognition elements, which play an important role in the control of many cellular processes and signaling pathways. It is useful to be able to predict positions of disordered residues and disordered regions in protein chains using protein sequence alone. A new method (IsUnstruct) based on the Ising model for prediction of disordered residues from protein sequence alone has been developed. According to this model, each residue can be in one of two states: ordered or disordered. The model is an approximation of the Ising model in which the interaction term between neighbors has been replaced by a penalty for changing between states (the energy of border). The IsUnstruct has been compared with other available methods and found to perform well. The method correctly finds 77% of disordered residues as well as 87% of ordered residues in the CASP8 database, and 72% of disordered residues as well as 85% of ordered residues in the DisProt database.
Analysis of the phase transition for the Ising model on the frustrated square lattice
NASA Astrophysics Data System (ADS)
Kalz, Ansgar; Honecker, Andreas; Moliner, Marion
2011-11-01
We analyze the phase transition of the frustrated J1-J2 Ising model with antiferromagnetic nearest- and strong next-nearest-neighbor interactions on the square lattice. Using extensive Monte Carlo simulations we show that the nature of the phase transition for 1/2
Noncyclic geometric quantum computation and preservation of entanglement for a two-qubit Ising model
NASA Astrophysics Data System (ADS)
Rangani Jahromi, H.; Amniat-Talab, M.
2015-10-01
After presenting an exact analytical solution of time-dependent Schrödinger equation, we study the dynamics of entanglement for a two-qubit Ising model. One of the spin qubits is driven by a static magnetic field applied in the direction of the Ising interaction, while the other is coupled with a rotating magnetic field. We also investigate how the entanglement can be controlled by changing the external parameters. Because of the important role of maximally entangled Bell states in quantum communication, we focus on the generalized Bell states as the initial states of the system. It is found that the entanglement evolution is independent of the initial Bell states. Moreover, we can preserve the initial maximal entanglement by adjusting the angular frequency of the rotating field or controlling the exchange coupling between spin qubits. Besides, our calculation shows that the entanglement dynamics is unaffected by the static magnetic field imposed in the direction of the Ising interaction. This is an interesting result, because, as we shall show below, this driving field can be used to control and manipulate the noncyclic geometric phase without affecting the system entanglement. Besides, the nonadiabatic and noncyclic geometric phase for evolved states of the present system are calculated and described in detail. In order to identify the unusable states for quantum communication, completely deviated from the initial maximally entangled states, we also study the fidelity between the initial Bell state and the evolved state of the system. Interestingly, we find that these unusable states can be detected by geometric quantum computation.
Long-range Ising and Kitaev models: phases, correlations and edge modes
NASA Astrophysics Data System (ADS)
Vodola, Davide; Lepori, Luca; Ercolessi, Elisa; Pupillo, Guido
2016-05-01
We analyze the quantum phases of the Ising chain with anti-ferromagnetic long-range interactions decaying with distance r as 1 /rα and of a related class of fermionic Hamiltonians generalising the Kitaev chain, with hopping and pairing terms long-range. We provide the phase diagram for all exponents α, based on an analysis of the entanglement entropy, the decay of correlation functions, and the edge modes in the case of open chains. We demonstrate that violations of the area law can occur for α < 1 , while correlation functions decay with a hybrid exponential and power-law behaviour. For the fermionic models we provide an exact analytical derivation for the decay of the correlation functions at every α. For the fermionic models we show that the edge modes, massless for α > 1 , acquire a mass for α < 1 . For the Ising chain a similar edge localization appears for the first and second excited states on the paramagnetic side of the phase diagram, where edge modes are not expected. We argue that, at least for the fermionic chains, these massive states correspond to the appearance of new phases, notably approached via quantum phase transitions without mass gap closure.
Automata and the susceptibility of the square lattice Ising model modulo powers of primes
NASA Astrophysics Data System (ADS)
Guttmann, A. J.; Maillard, J.-M.
2015-11-01
We study the full susceptibility of the Ising model modulo powers of primes. We find exact functional equations for the full susceptibility modulo these primes. Revisiting some lesser-known results on discrete finite automata, we show that these results can be seen as a consequence of the fact that, modulo 2 r , one cannot distinguish the full susceptibility from some simple diagonals of rational functions which reduce to algebraic functions modulo 2 r , and, consequently, satisfy exact functional equations modulo 2 r . We sketch a possible physical interpretation of these functional equations modulo 2 r as reductions of a master functional equation corresponding to infinite order symmetries such as the isogenies of elliptic curves. One relevant example is the Landen transformation which can be seen as an exact generator of the Ising model renormalization group. We underline the importance of studying a new class of functions corresponding to ratios of diagonals of rational functions: they reduce to algebraic functions modulo powers of primes and they may have solutions with natural boundaries. Dedicated to R J Baxter, for his 75th birthday.
Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system
NASA Astrophysics Data System (ADS)
Gong, Ming; Wen, Xueda; Sun, Guozhu; Zhang, Dan-Wei; Lan, Dong; Zhou, Yu; Fan, Yunyi; Liu, Yuhao; Tan, Xinsheng; Yu, Haifeng; Yu, Yang; Zhu, Shi-Liang; Han, Siyuan; Wu, Peiheng
2016-03-01
The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena.
Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system
Gong, Ming; Wen, Xueda; Sun, Guozhu; Zhang, Dan-Wei; Lan, Dong; Zhou, Yu; Fan, Yunyi; Liu, Yuhao; Tan, Xinsheng; Yu, Haifeng; Yu, Yang; Zhu, Shi-Liang; Han, Siyuan; Wu, Peiheng
2016-01-01
The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena. PMID:26951775
Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system.
Gong, Ming; Wen, Xueda; Sun, Guozhu; Zhang, Dan-Wei; Lan, Dong; Zhou, Yu; Fan, Yunyi; Liu, Yuhao; Tan, Xinsheng; Yu, Haifeng; Yu, Yang; Zhu, Shi-Liang; Han, Siyuan; Wu, Peiheng
2016-01-01
The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena. PMID:26951775
NASA Astrophysics Data System (ADS)
Gudyma, Iu.; Maksymov, A.; Spinu, L.
2015-10-01
The spin-crossover nanoparticles of different sizes and stochastic perturbations in external field taking into account the influence of the dimensionality of the lattice was studied. The analytical tools used for the investigation of spin-crossover system are based on an Ising-like model described using of the breathing crystal field concept. The changes of transition temperatures characterizing the systems' bistable properties for 2D and 3D lattices, and their dependence on its size and fluctuations strength were obtained. The state diagrams with hysteretic and non-hysteretic behavior regions have also been determined.
Nonequilibrium dynamics of arbitrary-range Ising models with decoherence: An exact analytic solution
NASA Astrophysics Data System (ADS)
Foss-Feig, Michael; Hazzard, Kaden R. A.; Bollinger, John J.; Rey, Ana Maria
2013-04-01
The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics. In a step toward understanding this interplay, we obtain an exact analytic solution for the nonequilibrium dynamics of Ising models with arbitrary couplings (and therefore in arbitrary dimension) and subject to local Markovian decoherence. Our solution shows that decoherence significantly degrades the nonclassical correlations developed during coherent Ising spin dynamics, which relax much faster than predicted by treating decoherence and interactions separately. We also show that the competition of decoherence and interactions induces a transition from oscillatory to overdamped dynamics that is absent at the single-particle or mean-field level. These calculations are applicable to ongoing quantum information and emulation efforts using a variety of atomic, molecular, optical, and solid-state systems. In particular, we apply our results to the NIST Penning trapped-ion experiment and show that the current experiment is capable of producing entanglement amongst hundreds of quantum spins.
Ising-nematic order in the bilinear-biquadratic model for the iron pnictides
NASA Astrophysics Data System (ADS)
Bilbao Ergueta, Patricia; Nevidomskyy, Andriy H.
2015-10-01
Motivated by the recent inelastic neutron scattering (INS) measurements in the iron pnictides which show a strong anisotropy of spin excitations even above the magnetic transition temperature TN, we study the spin dynamics within the frustrated Heisenberg model with biquadratic spin-spin exchange interactions. Using the Dyson-Maleev (DM) representation, which proves appropriate for all temperature regimes, we find that the spin-spin dynamical structure factors are in excellent agreement with experiment, exhibiting breaking of the C4 symmetry even into the paramagnetic region TN
Self-organizing Ising model of artificial financial markets with small-world network topology
NASA Astrophysics Data System (ADS)
Zhao, Haijie; Zhou, Jie; Zhang, Anghui; Su, Guifeng; Zhang, Yi
2013-01-01
We study a self-organizing Ising-like model of artificial financial markets with underlying small-world (SW) network topology. The asset price dynamics results from the collective decisions of interacting agents which are located on a small-world complex network (the nodes symbolize the agents of a financial market). The model incorporates the effects of imitation, the impact of external news and private information. We also investigate the influence of different network topologies, from regular lattice to random graph, on the asset price dynamics by adjusting the probability of the rewiring procedure. We find that a specific combination of model parameters reproduce main stylized facts of real-world financial markets.
Parity Symmetry and Parity Breaking in the Quantum Rabi Model with Addition of Ising Interaction
NASA Astrophysics Data System (ADS)
Wang, Qiong; He, Zhi; Yao, Chun-Mei
2015-04-01
We explore the possibility to generate new parity symmetry in the quantum Rabi model after a bias is introduced. In contrast to a mathematical treatment in a previous publication [J. Phys. A 46 (2013) 265302], we consider a physically realistic method by involving an additional spin into the quantum Rabi model to couple with the original spin by an Ising interaction, and then the parity symmetry is broken as well as the scaling behavior of the ground state by introducing a bias. The rule can be found that the parity symmetry is broken by introducing a bias and then restored by adding new degrees of freedom. Experimental feasibility of realizing the models under discussion is investigated. Supported by the National Natural Science Foundation of China under Grant Nos. 61475045 and 11347142, the Natural Science Foundation of Hunan Province, China under Grant No. 2015JJ3092
Macroscopic degeneracy and order in the 3D plaquette Ising model
NASA Astrophysics Data System (ADS)
Johnston, Desmond A.; Mueller, Marco; Janke, Wolfhard
2015-07-01
The purely plaquette 3D Ising Hamiltonian with the spins living at the vertices of a cubic lattice displays several interesting features. The symmetries of the model lead to a macroscopic degeneracy of the low-temperature phase and prevent the definition of a standard magnetic order parameter. Consideration of the strongly anisotropic limit of the model suggests that a layered, “fuki-nuke” order still exists and we confirm this with multi-canonical simulations. The macroscopic degeneracy of the low-temperature phase also changes the finite-size scaling corrections at the first-order transition in the model and we see this must be taken into account when analyzing our measurements.
Annealed Ising model with site dilution on self-similar structures
NASA Astrophysics Data System (ADS)
Silva, V. S. T.; Andrade, R. F. S.; Salinas, S. R.
2014-11-01
We consider an Ising model on the triangular Apollonian network (AN), with a thermalized distribution of vacant sites. The statistical problem is formulated in a grand canonical ensemble, in terms of the temperature T and a chemical potential μ associated with the concentration of active magnetic sites. We use a well-known transfer-matrix method, with a number of adaptations, to write recursion relations between successive generations of this hierarchical structure. We also investigate the analogous model on the diamond hierarchical lattice (DHL). From the numerical analysis of the recursion relations, we obtain various thermodynamic quantities. In the μ →∞ limit, we reproduce the results for the uniform models: in the AN, the system is magnetically ordered at all temperatures, while in the DHL there is a ferromagnetic-paramagnetic transition at a finite value of T . Magnetic ordering, however, is shown to disappear for sufficiently large negative values of the chemical potential.
Kriz, Igor; Loebl, Martin; Somberg, Petr
2013-05-15
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.
Theory and simulation of the dynamic heat capacity of the east Ising model.
Brown, Jonathan R; McCoy, John D; Borchers, Brian
2010-08-14
A recently developed methodology for the calculation of the dynamic heat capacity from simulation is applied to the east Ising model. Results show stretched exponential relaxation with the stretching exponent, beta, decreasing with decreasing temperature. For low temperatures, the logarithm of the relaxation time is approximately proportional to the inverse of the temperature squared, which is the theoretical limiting behavior predicted by theories of facilitated dynamics. In addition, an analytical approach is employed where the overall relaxation is a composite of relaxation processes of subdomains, each with their own characteristic time. Using a Markov chain method, these times are computed both numerically and in closed form. The Markov chain results are seen to match the simulations at low temperatures and high frequencies. The dynamics of the east model are tracked very well by this analytic procedure, and it is possible to associate features of the spectrum of the dynamic heat capacity with specific domain relaxation events. PMID:20707576
A set of exactly solvable Ising models with half-odd-integer spin
NASA Astrophysics Data System (ADS)
Rojas, Onofre; de Souza, S. M.
2009-03-01
We present a set of exactly solvable Ising models, with half-odd-integer spin- S on a square-type lattice including a quartic interaction term in the Hamiltonian. The particular properties of the mixed lattice, associated with mixed half-odd-integer spin- (S,1/2) and only nearest-neighbor interaction, allow us to map this system either onto a purely spin-1/2 lattice or onto a purely spin- S lattice. By imposing the condition that the mixed half-odd-integer spin- (S,1/2) lattice must have an exact solution, we found a set of exact solutions that satisfy the free fermion condition of the eight vertex model. The number of solutions for a general half-odd-integer spin- S is given by S+1/2. Therefore we conclude that this transformation is equivalent to a simple spin transformation which is independent of the coordination number.
Missing mass approximations for the partition function of stimulus driven Ising models
Haslinger, Robert; Ba, Demba; Galuske, Ralf; Williams, Ziv; Pipa, Gordon
2013-01-01
Ising models are routinely used to quantify the second order, functional structure of neural populations. With some recent exceptions, they generally do not include the influence of time varying stimulus drive. Yet if the dynamics of network function are to be understood, time varying stimuli must be taken into account. Inclusion of stimulus drive carries a heavy computational burden because the partition function becomes stimulus dependent and must be separately calculated for all unique stimuli observed. This potentially increases computation time by the length of the data set. Here we present an extremely fast, yet simply implemented, method for approximating the stimulus dependent partition function in minutes or seconds. Noting that the most probable spike patterns (which are few) occur in the training data, we sum partition function terms corresponding to those patterns explicitly. We then approximate the sum over the remaining patterns (which are improbable, but many) by casting it in terms of the stimulus modulated missing mass (total stimulus dependent probability of all patterns not observed in the training data). We use a product of conditioned logistic regression models to approximate the stimulus modulated missing mass. This method has complexity of roughly O(LNNpat) where is L the data length, N the number of neurons and Npat the number of unique patterns in the data, contrasting with the O(L2N) complexity of alternate methods. Using multiple unit recordings from rat hippocampus, macaque DLPFC and cat Area 18 we demonstrate our method requires orders of magnitude less computation time than Monte Carlo methods and can approximate the stimulus driven partition function more accurately than either Monte Carlo methods or deterministic approximations. This advance allows stimuli to be easily included in Ising models making them suitable for studying population based stimulus encoding. PMID:23898262
NASA Astrophysics Data System (ADS)
Ramazanov, M. K.; Murtazaev, A. K.; Magomedov, M. A.
2016-05-01
The thermodynamic and critical properties, and phase transitions of two-dimensional Ising model on a square lattice with competing interactions are investigated by the Monte Carlo method. Estimations are made for the magnitude relations of the next-nearest-neighbor and nearest-neighbor exchange interactions r=J2/J1 in the value ranges of 0.1≤r≤1.0. The anomalies of thermodynamic observables are shown to be present in this model on the interval 0.45≤r≤0.5. The phase diagram for the dependence of the critical temperature on a value of next-nearest neighbor interaction is plotted. A phase transition for all values in the interval 0.45≤r≤0.5 is shown to be a second order. Our data show that the temperature of the heat capacity maximum at r=0.5 tends to a finite value. The static critical exponents of the heat capacity α, susceptibility γ, order parameter β, correlation length ν, and the Fisher exponent η are calculated by means of the finite-size scaling theory. It is found that the change in next-nearest neighbor interaction value in the range 0.7≤r≤1.0 leads to nonuniversal critical behavior.
Highly optimized simulations on single- and multi-GPU systems of the 3D Ising spin glass model
NASA Astrophysics Data System (ADS)
Lulli, M.; Bernaschi, M.; Parisi, G.
2015-11-01
We present a highly optimized implementation of a Monte Carlo (MC) simulator for the three-dimensional Ising spin-glass model with bimodal disorder, i.e., the 3D Edwards-Anderson model running on CUDA enabled GPUs. Multi-GPU systems exchange data by means of the Message Passing Interface (MPI). The chosen MC dynamics is the classic Metropolis one, which is purely dissipative, since the aim was the study of the critical off-equilibrium relaxation of the system. We focused on the following issues: (i) the implementation of efficient memory access patterns for nearest neighbours in a cubic stencil and for lagged-Fibonacci-like pseudo-Random Numbers Generators (PRNGs); (ii) a novel implementation of the asynchronous multispin-coding Metropolis MC step allowing to store one spin per bit and (iii) a multi-GPU version based on a combination of MPI and CUDA streams. Cubic stencils and PRNGs are two subjects of very general interest because of their widespread use in many simulation codes.
Hysteresis in random-field Ising model on a Bethe lattice with a mixed coordination number
NASA Astrophysics Data System (ADS)
Shukla, Prabodh; Thongjaomayum, Diana
2016-06-01
We study zero-temperature hysteresis in the random-field Ising model on a Bethe lattice where a fraction c of the sites have coordination number z = 4 while the remaining fraction 1-c have z = 3. Numerical simulations as well as probabilistic methods are used to show the existence of critical hysteresis for all values of c\\gt 0. This extends earlier results for c = 0 and c = 1 to the entire range 0≤slant c≤slant 1, and provides new insight in non-equilibrium critical phenomena. Our analysis shows that a spanning avalanche can occur on a lattice even in the absence of a spanning cluster of z = 4 sites.
The hypergeometric series for the partition function of the 2D Ising model
NASA Astrophysics Data System (ADS)
Viswanathan, G. M.
2015-07-01
In 1944 Onsager published the formula for the partition function of the Ising model for the infinite square lattice. He was able to express the internal energy in terms of a special function, but he left the free energy as a definite integral. Seven decades later, the partition function and free energy have yet to be written in closed form, even with the aid of special functions. Here we evaluate the definite integral explicitly, using hypergeometric series. Let β denote the reciprocal temperature, J the coupling and f the free energy per spin. We prove that - β f = \\ln(2 \\cosh 2K) - κ2 ~ {_4F_3} \\big[~ 1,~1,~3/2,~3/2 ~~~2,~2,~2 ;16 κ2 ~\\big] ~ , where pFq is the generalized hypergeometric function, K = βJ, and 2κ = tanh 2K sech 2K.
Effective-field theory on the kinetic spin-3/2 Ising model
NASA Astrophysics Data System (ADS)
Shi, Xiaoling; Qi, Yang
2015-11-01
The effective-field theory (EFT) is used to study the dynamical response of the kinetic spin-3/2 Ising model in the presence of a sinusoidal oscillating magnetic field. The effective-field dynamic equations are given for the honeycomb lattices (Z = 3). The dynamic order parameter, the dynamic quadrupole moment are calculated. We have found that the behavior of the system strongly depends on the crystal field interaction D. The dynamic phase boundaries are obtained, and there is no dynamic tricritical point on the dynamic phase transition line. The results are also compared with previous results which obtained from the mean-field theory (MFT) and the effective-field theory (EFT) for the square lattices (Z = 4). Different dynamic phase transition lines show that the thermal fluctuations are a key factor of the dynamic phase transition.
Long-range random transverse-field Ising model in three dimensions
NASA Astrophysics Data System (ADS)
Kovács, István A.; Juhász, Róbert; Iglói, Ferenc
2016-05-01
We consider the random transverse-field Ising model in d =3 dimensions with long-range ferromagnetic interactions which decay as a power α >d with the distance. Using a variant of the strong-disorder renormalization group method we study numerically the phase-transition point from the paramagnetic side. We find that the fixed point controlling the transition is of the strong-disorder type, and based on experience with other similar systems, we expect the results to be qualitatively correct, but probably not asymptotically exact. The distribution of the (sample dependent) pseudocritical points is found to scale with 1 /lnL , L being the linear size of the sample. Similarly, the critical magnetization scales with (lnL) χ/Ld and the excitation energy behaves as L-α. Using extreme-value statistics we argue that extrapolating from the ferromagnetic side the magnetization approaches a finite limiting value and thus the transition is of mixed order.
A theory of solving TAP equations for Ising models with general invariant random matrices
NASA Astrophysics Data System (ADS)
Opper, Manfred; Çakmak, Burak; Winther, Ole
2016-03-01
We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields an effective dynamics of a single variable trajectory. Our main novel contribution is the expression for the implicit memory term of the dynamics for general invariant ensembles. By subtracting these terms, that depend on magnetizations at previous time steps, the implicit memory terms cancel making the iteration dependent on a Gaussian distributed field only. The TAP magnetizations are stable fixed points if a de Almeida-Thouless stability criterion is fulfilled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble.
Convergence of the Equi-Energy Sampler and Its Application to the Ising Model.
Hua, Xia; Kou, S C
2011-10-01
We provide a complete proof of the convergence of a recently developed sampling algorithm called the equi-energy (EE) sampler (Kou, Zhou, and Wong, 2006) in the case that the state space is countable. We show that in a countable state space, each sampling chain in the EE sampler is strongly ergodic a.s. with the desired steady-state distribution. Furthermore, all chains satisfy the individual ergodic property. We apply the EE sampler to the Ising model to test its efficiency, comparing it with the Metropolis algorithm and the parallel tempering algorithm. We observe that the dynamic exponent of the EE sampler is significantly smaller than those of parallel tempering and the Metropolis algorithm, demonstrating the high efficiency of the EE sampler. PMID:21969801
Universality Class of the Nishimori Point in the 2D +/-J Random-Bond Ising Model
NASA Astrophysics Data System (ADS)
Honecker, A.; Picco, M.; Pujol, P.
2001-07-01
We study the universality class of the Nishimori point in the 2D +/-J random-bond Ising model by means of the numerical transfer-matrix method. Using the domain-wall free energy, we locate the position of the fixed point along the Nishimori line at the critical concentration value pc = 0.1094+/-0.0002 and estimate ν = 1.33+/-0.03. Then, we obtain the exponents for the moments of the spin-spin correlation functions as well as the value for the central charge c = 0.464+/-0.004. The main qualitative result is the fact that percolation is now excluded as a candidate for describing the universality class of this fixed point.
Universality class of the Nishimori point in the 2D +/- J random-bond Ising model.
Honecker, A; Picco, M; Pujol, P
2001-07-23
We study the universality class of the Nishimori point in the 2D +/- J random-bond Ising model by means of the numerical transfer-matrix method. Using the domain-wall free energy, we locate the position of the fixed point along the Nishimori line at the critical concentration value p(c) = 0.1094 +/- 0.0002 and estimate nu = 1.33 +/- 0.03. Then, we obtain the exponents for the moments of the spin-spin correlation functions as well as the value for the central charge c = 0.464 +/- 0.004. The main qualitative result is the fact that percolation is now excluded as a candidate for describing the universality class of this fixed point. PMID:11461639
Non-equilibrium steady states in two-temperature Ising models with Kawasaki dynamics
NASA Astrophysics Data System (ADS)
Borchers, Nick; Pleimling, Michel; Zia, R. K. P.
2013-03-01
From complex biological systems to a simple simmering pot, thermodynamic systems held out of equilibrium are exceedingly common in nature. Despite this, a general theory to describe these types of phenomena remains elusive. In this talk, we explore a simple modification of the venerable Ising model in hopes of shedding some light on these issues. In both one and two dimensions, systems attached to two distinct heat reservoirs exhibit many of the hallmarks of phase transition. When such systems settle into a non-equilibrium steady-state they exhibit numerous interesting phenomena, including an unexpected ``freezing by heating.'' There are striking and surprising similarities between the behavior of these systems in one and two dimensions, but also intriguing differences. These phenomena will be explored and possible approaches to understanding the behavior will be suggested. Supported by the US National Science Foundation through Grants DMR-0904999, DMR-1205309, and DMR-1244666
Stochastic Resonance in the Ising Model on a BARABÁSI-ALBERT Network
NASA Astrophysics Data System (ADS)
Krawiecki, A.
Stochastic resonance is investigated in the Ising model with ferromagnetic coupling on a Barabási-Albert network, subjected to weak periodic magnetic field. Spectral power amplification as a function of temperature shows strong dependence on the number of nodes, which is related to the dependence of the critical temperature for the ferromagnetic phase transition, and on the frequency of the periodic signal. Double maxima of the spectral power amplification evaluated from the time-dependent magnetization are observed for intermediate frequencies of the periodic signal, which are also dependent on the number of nodes. In the thermodynamic limit, the height of the maxima decreases to zero and stochastic resonance disappears. Results of numerical simulations are in qualitative agreement with predictions of the linear response theory in the mean-field approximation.
Dynamical Phase Transition in the Ising Model on a Scale-Free Network
NASA Astrophysics Data System (ADS)
Krawiecki, A.
Dynamical phase transition in the Ising model on a Barabási-Albert network under the influence of periodic magnetic field is studied using Monte-Carlo simulations. For a wide range of the system sizes N and the field frequencies, approximate phase borders between dynamically ordered and disordered phases are obtained on a plane h (field amplitude) versus T/Tc (temperature normalized to the static critical temperature without external field, Tc∝lnN). On these borders, second- or first-order transitions occur, for parameter ranges separated by a tricritical point. For all frequencies of the magnetic field, position of the tricritical point is shifted toward higher values of T/Tc and lower values of h with increasing system size, i.e. the range of critical parameters corresponding to the first-order transition is broadened.
Almost Gibbsianness and Parsimonious Description of the Decimated 2d-Ising Model
NASA Astrophysics Data System (ADS)
Le Ny, Arnaud
2013-07-01
In this paper, we complete and provide details for the existing characterizations of the decimation of the Ising model on {Z}2 in the generalized Gibbs context. We first recall a few features of the Dobrushin program of restoration of Gibbsianness and present the construction of global specifications consistent with the extremal decimated measures. We use them to prove that these renormalized measures are almost Gibbsian at any temperature and to analyse in detail its convex set of DLR measures. We also recall the weakly Gibbsian description and complete it using a potential that admits a quenched correlation decay, i.e. a well-defined configuration-dependent length beyond which this potential decays exponentially. We use these results to incorporate these decimated measures in the new framework of parsimonious random fields that has been recently developed to investigate probability aspects related to neurosciences.
Britton, Joseph W; Sawyer, Brian C; Keith, Adam C; Wang, C-C Joseph; Freericks, James K; Uys, Hermann; Biercuk, Michael J; Bollinger, John J
2012-04-26
The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed-matter systems, potentially including high-temperature superconductivity. However, many properties of exotic, strongly correlated spin systems, such as spin liquids, have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N ≈ 30 particles. Feynman predicted that a quantum simulator--a special-purpose 'analogue' processor built using quantum bits (qubits)--would be inherently suited to solving such problems. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach, but simulations allowing controlled, tunable interactions between spins localized on two- or three-dimensional lattices of more than a few tens of qubits have yet to be demonstrated, in part because of the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin-spin interaction, J(i,j), on a naturally occurring, two-dimensional triangular crystal lattice of hundreds of spin-half particles (beryllium ions stored in a Penning trap). This is a computationally relevant scale more than an order of magnitude larger than previous experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction J(i,j) proportional variant d(-a)(i,j), where 0 ≤ a ≤ 3 and d(i,j) is the distance between spin pairs. These power laws correspond physically to infinite-range (a = 0), Coulomb-like (a = 1), monopole-dipole (a = 2) and dipole-dipole (a = 3) couplings. Experimentally, we demonstrate excellent agreement with a theory for 0.05 ≲ a ≲ 1.4. This demonstration, coupled with the high spin count, excellent quantum control and low technical complexity of the Penning trap, brings within reach the simulation of otherwise computationally intractable problems in quantum magnetism
NASA Astrophysics Data System (ADS)
Cabrera, I.; Thompson, J. D.; Coldea, R.; Prabhakaran, D.; Bewley, R. I.; Guidi, T.; Rodriguez-Rivera, J. A.; Stock, C.
2014-07-01
The quasi-one-dimensional (1D) Ising ferromagnet CoNb2O6 has recently been driven via applied transverse magnetic fields through a continuous quantum phase transition from spontaneous magnetic order to a quantum paramagnet, and dramatic changes were observed in the spin dynamics, characteristic of weakly perturbed 1D Ising quantum criticality. We report here extensive single-crystal inelastic neutron scattering measurements of the magnetic excitations throughout the three-dimensional (3D) Brillouin zone in the quantum paramagnetic phase just above the critical field to characterize the effects of the finite interchain couplings. In this phase, we observe that excitations have a sharp, resolution-limited line shape at low energies and over most of the dispersion bandwidth, as expected for spin-flip quasiparticles. We map the full bandwidth along the strongly dispersive chain direction and resolve clear modulations of the dispersions in the plane normal to the chains, characteristic of frustrated interchain couplings in an antiferromagnetic isosceles triangular lattice. The dispersions can be well parametrized using a linear spin-wave model that includes interchain couplings and further neighbor exchanges. The observed dispersion bandwidth along the chain direction is smaller than that predicted by a linear spin-wave model using exchange values determined at zero field, and this effect is attributed to quantum renormalization of the dispersion beyond the spin-wave approximation in fields slightly above the critical field, where quantum fluctuations are still significant.
NASA Astrophysics Data System (ADS)
Hayden, Lorien; Sethna, James
We systematically analyze the nonlinear invariant scaling variables at bifurcations in the renormalization-group flow, and apply our methods to the two-dimensional random-field Ising model (RFIM). At critical points, the universal scaling functions are usually written in terms of homogeneous invariant combinations of variables, like Ltν in the finite-size scaling form for the magnetization M (T | L) ~t-β M (Ltν) , where t ~Tc - T . The renormalization-group flow for the RFIM has a pitchfork bifurcation in two dimensions, where the correlation length has been argued to diverge exponentially, ξ ~ exp 1 / 2 At2 , leading to the invariant scaling combination L / ξ ~ L / exp 1 / 2 At2 . Our analysis, inspired by normal-form theory, suggests that this exponential divergence can take a richer, more general scaling form at a generic pitchfork bifurcation. We explore possible consequences for simulations. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. . DGE-1144153.
Highlighting the Structure-Function Relationship of the Brain with the Ising Model and Graph Theory
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
Highlighting the structure-function relationship of the brain with the Ising model and graph theory.
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
A fully Bayesian hidden Ising model for ChIP-seq data analysis.
Mo, Qianxing
2012-01-01
Chromatin immunoprecipitation followed by next generation sequencing (ChIP-seq) is a powerful technique that is being used in a wide range of biological studies including genome-wide measurements of protein-DNA interactions, DNA methylation, and histone modifications. The vast amount of data and biases introduced by sequencing and/or genome mapping pose new challenges and call for effective methods and fast computer programs for statistical analysis. To systematically model ChIP-seq data, we build a dynamic signal profile for each chromosome and then model the profile using a fully Bayesian hidden Ising model. The proposed model naturally takes into account spatial dependency and global and local distributions of sequence tags. It can be used for one-sample and two-sample analyses. Through model diagnosis, the proposed method can detect falsely enriched regions caused by sequencing and/or mapping errors, which is usually not offered by the existing hypothesis-testing-based methods. The proposed method is illustrated using 3 transcription factor (TF) ChIP-seq data sets and 2 mixed ChIP-seq data sets and compared with 4 popular and/or well-documented methods: MACS, CisGenome, BayesPeak, and SISSRs. The results indicate that the proposed method achieves equivalent or higher sensitivity and spatial resolution in detecting TF binding sites with false discovery rate at a much lower level. PMID:21914728
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.
NASA Astrophysics Data System (ADS)
Huang, Ran; Zhang, Ling; Chen, Chong; Wu, Chengjie; Yan, Linyin
2015-07-01
The ferromagnetic Ising spins are modeled on a recursive lattice constructed from random-angled rhombus units with stochastic configurations, to study the magnetic properties of the bulk Fe-based metallic glass. The integration of spins on the structural glass model well represents the magnetic moments in the glassy metal. The model is exactly solved by the recursive calculation technique. The magnetization of the amorphous Ising spins, i.e. the glassy metallic magnet is investigated by our modeling and calculation on a theoretical base. The results show that the glassy metallic magnets have a lower Curie temperature, weaker magnetization, and higher entropy compared to the regular ferromagnet in crystal form. These findings can be understood with the randomness of the amorphous system, and agree well with other experimental observations.
Ising-like model for the two-step spin-crossover
NASA Astrophysics Data System (ADS)
Bousseksou, A.; Nasser, J.; Linares, J.; Boukheddaden, K.; Varret, F.
1992-07-01
We have analyzed an Ising-like model, in the mean-field approach, involving two “antiferromagnetically” coupled sublattices. This model simulates the so-called “two-step” spin-crossover transition, for which a precise definition is given. If both sublattices are equivalent, it implies a spontaneous breaking of symmetry which may occur within a temperature range limited by two “Néel températures”. It, also predicts a simultaneous reversal of the magnetization of the sublattices (if they are unequivalent) at a “characteristic” value of temperature. These features are analyzed simultaneously with some details. The present model fits and explains well the available experimental data concerning [ Fe(2-pic)_3] Cell_2- EtOH and Fe^II[ 5NO2 sal N(1, 4, 7, 10)] . Nous avons analysé un modèle de type Ising, à deux sous-réseaux couplés “antiferromagnétiquement”, dans l'approximation du champ moyen. Ce modèle permet de bien reproduire les transitions de spin “en deux étapes”, dont nous donnons une définition précise. Lorsque les deux sous-réseaux sont équivalents, il implique une brisure spontanée de symétrie qui peut intervenir dans un domaine de température limité par deux “températures de Néel”. De plus, lorsqu'ils sont inéquivalents, il prédit le renversement simultané de l' “aimantation” des deux sous-réseaux pour une valeur “caractéristique” de la température. Nous avons analysé en détail l'ensemble de ces effets. Ce modèle nous a permis d'ajuster et de discuter les résultats expérimentaux disponibles concernant [ Fe(2-pic)_3] Cell_2- EtOH et Fe^II[ 5NO2 sal N(1, 4, 7, 10)] .
Ising-like transitions in the O(n) loop model on the square lattice.
Fu, Zhe; Guo, Wenan; Blöte, Henk W J
2013-05-01
We explore the phase diagram of the O(n) loop model on the square lattice in the (x,n) plane, where x is the weight of a lattice edge covered by a loop. These results are based on transfer-matrix calculations and finite-size scaling. We express the correlation length associated with the staggered loop density in the transfer-matrix eigenvalues. The finite-size data for this correlation length, combined with the scaling formula, reveal the location of critical lines in the diagram. For n>2 we find Ising-like phase transitions associated with the onset of a checkerboardlike ordering of the elementary loops, i.e., the smallest possible loops, with the size of an elementary face, which cover precisely one-half of the faces of the square lattice at the maximum loop density. In this respect, the ordered state resembles that of the hard-square lattice gas with nearest-neighbor exclusion, and the finiteness of n represents a softening of its particle-particle potentials. We also determine critical points in the range -2≤n≤2. It is found that the topology of the phase diagram depends on the set of allowed vertices of the loop model. Depending on the choice of this set, the n>2 transition may continue into the dense phase of the n≤2 loop model, or continue as a line of n≤2 O(n) multicritical points. PMID:23767498
Information Transfer and Criticality in the Ising Model on the Human Connectome
Marinazzo, Daniele; Pellicoro, Mario; Wu, Guorong; Angelini, Leonardo; Cortés, Jesús M.; Stramaglia, Sebastiano
2014-01-01
We implement the Ising model on a structural connectivity matrix describing the brain at two different resolutions. Tuning the model temperature to its critical value, i.e. at the susceptibility peak, we find a maximal amount of total information transfer between the spin variables. At this point the amount of information that can be redistributed by some nodes reaches a limit and the net dynamics exhibits signature of the law of diminishing marginal returns, a fundamental principle connected to saturated levels of production. Our results extend the recent analysis of dynamical oscillators models on the connectome structure, taking into account lagged and directional influences, focusing only on the nodes that are more prone to became bottlenecks of information. The ratio between the outgoing and the incoming information at each node is related to the the sum of the weights to that node and to the average time between consecutive time flips of spins. The results for the connectome of 66 nodes and for that of 998 nodes are similar, thus suggesting that these properties are scale-independent. Finally, we also find that the brain dynamics at criticality is organized maximally to a rich-club w.r.t. the network of information flows. PMID:24705627
Nonbacktracking operator for the Ising model and its applications in systems with multiple states
NASA Astrophysics Data System (ADS)
Zhang, Pan
2015-04-01
The nonbacktracking operator for a graph is the adjacency matrix defined on directed edges of the graph. The operator was recently shown to perform optimally in spectral clustering in sparse synthetic graphs and have a deep connection to belief propagation algorithm. In this paper we consider nonbacktracking operator for Ising model on a general graph with a general coupling distribution and study the spectrum of this operator analytically. We show that spectral algorithms based on this operator is equivalent to belief propagation algorithm linearized at the paramagnetic fixed point and recovers replica-symmetry results on phase boundaries obtained by replica methods. This operator can be applied directly to systems with multiple states like Hopfield model. We show that spectrum of the operator can be used to determine number of patterns that stored successfully in the network, and the associated eigenvectors can be used to retrieve all the patterns simultaneously. We also give an example on how to control the Hopfield model, i.e., making network more sparse while keeping patterns stable, using the nonbacktracking operator and matrix perturbation theory.
Ising-like agent-based technology diffusion model: Adoption patterns vs. seeding strategies
NASA Astrophysics Data System (ADS)
Laciana, Carlos E.; Rovere, Santiago L.
2011-03-01
The well-known Ising model used in statistical physics was adapted to a social dynamics context to simulate the adoption of a technological innovation. The model explicitly combines (a) an individual's perception of the advantages of an innovation and (b) social influence from members of the decision-maker's social network. The micro-level adoption dynamics are embedded into an agent-based model that allows exploration of macro-level patterns of technology diffusion throughout systems with different configurations (number and distributions of early adopters, social network topologies). In the present work we carry out many numerical simulations. We find that when the gap between the individual's perception of the options is high, the adoption speed increases if the dispersion of early adopters grows. Another test was based on changing the network topology by means of stochastic connections to a common opinion reference (hub), which resulted in an increment in the adoption speed. Finally, we performed a simulation of competition between options for both regular and small world networks.
Belief-propagation algorithm and the Ising model on networks with arbitrary distributions of motifs
NASA Astrophysics Data System (ADS)
Yoon, S.; Goltsev, A. V.; Dorogovtsev, S. N.; Mendes, J. F. F.
2011-10-01
We generalize the belief-propagation algorithm to sparse random networks with arbitrary distributions of motifs (triangles, loops, etc.). Each vertex in these networks belongs to a given set of motifs (generalization of the configuration model). These networks can be treated as sparse uncorrelated hypergraphs in which hyperedges represent motifs. Here a hypergraph is a generalization of a graph, where a hyperedge can connect any number of vertices. These uncorrelated hypergraphs are treelike (hypertrees), which crucially simplifies the problem and allows us to apply the belief-propagation algorithm to these loopy networks with arbitrary motifs. As natural examples, we consider motifs in the form of finite loops and cliques. We apply the belief-propagation algorithm to the ferromagnetic Ising model with pairwise interactions on the resulting random networks and obtain an exact solution of this model. We find an exact critical temperature of the ferromagnetic phase transition and demonstrate that with increasing the clustering coefficient and the loop size, the critical temperature increases compared to ordinary treelike complex networks. However, weak clustering does not change the critical behavior qualitatively. Our solution also gives the birth point of the giant connected component in these loopy networks.
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
Domain-size heterogeneity in the Ising model: Geometrical and thermal transitions.
de la Rocha, André R; de Oliveira, Paulo Murilo C; Arenzon, Jeferson J
2015-04-01
A measure of cluster size heterogeneity (H), introduced by Lee et al. [Phys. Rev. E 84, 020101 (2011)] in the context of explosive percolation, was recently applied to random percolation and to domains of parallel spins in the Ising and Potts models. It is defined as the average number of different domain sizes in a given configuration and a new exponent was introduced to explain its scaling with the size of the system. In thermal spin models, however, physical clusters take into account the temperature-dependent correlation between neighboring spins and encode the critical properties of the phase transition. We here extend the measure of H to these clusters and, moreover, present new results for the geometric domains for both d=2 and 3. We show that the heterogeneity associated with geometric domains has a previously unnoticed double peak, thus being able to detect both the thermal and percolative transitions. An alternative interpretation for the scaling of H that does not introduce a new exponent is also proposed. PMID:25974445
Domain-size heterogeneity in the Ising model: Geometrical and thermal transitions
NASA Astrophysics Data System (ADS)
de la Rocha, André R.; de Oliveira, Paulo Murilo C.; Arenzon, Jeferson J.
2015-04-01
A measure of cluster size heterogeneity (H ), introduced by Lee et al. [Phys. Rev. E 84, 020101 (2011), 10.1103/PhysRevE.84.020101] in the context of explosive percolation, was recently applied to random percolation and to domains of parallel spins in the Ising and Potts models. It is defined as the average number of different domain sizes in a given configuration and a new exponent was introduced to explain its scaling with the size of the system. In thermal spin models, however, physical clusters take into account the temperature-dependent correlation between neighboring spins and encode the critical properties of the phase transition. We here extend the measure of H to these clusters and, moreover, present new results for the geometric domains for both d =2 and 3. We show that the heterogeneity associated with geometric domains has a previously unnoticed double peak, thus being able to detect both the thermal and percolative transitions. An alternative interpretation for the scaling of H that does not introduce a new exponent is also proposed.
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).
Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks
NASA Astrophysics Data System (ADS)
Krasnytska, M.; Berche, B.; Holovatch, Yu; Kenna, R.
2016-04-01
We analyse the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as P(k) ˜ k -λ . We are interested in zeros of the partition function in the cases of complex temperature or complex external field (Fisher and Lee-Yang zeros respectively). For the model on an annealed scale-free network, we find an integral representation for the partition function which, in the case λ > 5, reproduces the zeros for the Ising model on a complete graph. For 3 < λ < 5 we derive the λ-dependent angle at which the Fisher zeros impact onto the real temperature axis. This, in turn, gives access to the λ-dependent universal values of the critical exponents and critical amplitudes ratios. Our analysis of the Lee-Yang zeros reveals a difference in their behaviour for the Ising model on a complete graph and on an annealed scale-free network when 3 < λ < 5. Whereas in the former case the zeros are purely imaginary, they have a non zero real part in latter case, so that the celebrated Lee-Yang circle theorem is violated.
Study of spin crossover nanoparticles thermal hysteresis using FORC diagrams on an Ising-like model
NASA Astrophysics Data System (ADS)
Atitoaie, Alexandru; Tanasa, Radu; Stancu, Alexandru; Enachescu, Cristian
2014-11-01
Recent developments in the synthesis and characterization of spin crossover (SCO) nanoparticles and their prospects of switching at molecular level turned these bistable compounds into possible candidates for replacing the materials used in recording media industry for development of solid state pressure and temperature sensors or for bringing contributions in engineering. Compared to bulk samples with the same chemical structure, SCO nanoparticles display different characteristics of the hysteretic and relaxation properties like the shift of the transition temperature towards lower values along with decrease of the hysteresis width with nanoparticles size. Using an Ising-like model with specific boundary conditions within a Monte Carlo procedure, we here reproduce most of the hysteretic properties of SCO nanoparticles by considering the interaction between spin crossover edge molecules and embedding surfactant molecules and we propose a complex analysis concerning the effect of the interactions and sizes during the thermal transition in systems of SCO nanoparticles by using the First Order Reversal Curves diagram method and by comparison with similar effects in mixed crystal systems.
The dynamic critical properties of the spin-2 Ising model on a bilayer square lattice
NASA Astrophysics Data System (ADS)
Temizer, Ümüt; Yarar, Semih; Tülek, Mesimi
2016-05-01
The spin-2 Ising model is investigated for the ferromagnetic/ferromagnetic (FM/FM), antiferromagnetic/ferromagnetic (AFM/FM) and antiferromagnetic/antiferromagnetic (AFM/AFM) interactions on the two-layer square lattice by using the Glauber-type stochastic dynamics. The system is in contact with a heat bath at temperature T, and the exchange of energy with the heat bath occurs via one-spin flip. By employing the Master equation and Glauber transition rates, the dynamic equations of the system are obtained. These equations are solved by using the numerical methods. First, we investigate the average order parameters as a function of the time to find the phases in the system. Then, the temperature-dependence of the dynamic order parameters is examined to obtain the dynamic phase transition temperatures. The dynamic phase diagrams are presented on the different planes. According to the values of the system parameters, a variety of dynamic critical points such as tricritical point, triple point, quadruple point, critical end point, double critical end point, zero-temperature critical point, multicritical point and tetracritical point are obtained. The reentrant behavior is seen in the system for the AFM/AFM interaction. Finally, we also investigate the influence of the oscillating field frequency on the dynamic phase diagrams in detail.
Minority-spin dynamics in the nonhomogeneous Ising model: Diverging time scales and exponents
NASA Astrophysics Data System (ADS)
Mullick, Pratik; Sen, Parongama
2016-05-01
We investigate the dynamical behavior of the Ising model under a zero-temperature quench with the initial fraction of up spins 0 ≤x ≤1 . In one dimension, the known results for persistence probability are verified; it shows algebraic decay for both up and down spins asymptotically with different exponents. It is found that the conventional finite-size scaling is valid here. In two dimensions, however, the persistence probabilities are no longer algebraic; in particular for x ≤0.5 , persistence for the up (minority) spins shows the behavior Pmin(t ) ˜t-γexp[-(t/τ ) δ] with time t , while for the down (majority) spins, Pmaj(t ) approaches a finite value. We find that the timescale τ diverges as (xc-x ) -λ, where xc=0.5 and λ ≃2.31 . The exponent γ varies as θ2 d+c0(xc-x ) β where θ2 d≃0.215 is very close to the persistence exponent in two dimensions; β ≃1 . The results in two dimensions can be understood qualitatively by studying the exit probability, which for different system size is found to have the form E (x ) =f [(x/-xc xc) L1 /ν] , with ν ≈1.47 . This result suggests that τ ˜Lz ˜ , where z ˜=λ/ν =1.57 ±0.11 is an exponent not explored earlier.
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.
Quantum correlated cluster mean-field theory applied to the transverse Ising model
NASA Astrophysics Data System (ADS)
Zimmer, F. M.; Schmidt, M.; Maziero, Jonas
2016-06-01
Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.
Spinodals of the Ising model on the order-4 pentagonal tiling of the hyperbolic plane
NASA Astrophysics Data System (ADS)
Richards, Howard L.
In the Euclidean plane, the Ising model on a regular lattice does not have a true spinodal - that is, there is no local minimum of the free energy that persists forever (in the limit of infinitely large systems) except for the global minimum, which characterizes the stable state. However, a local minimum can persist for a very long time, so the minimum can be referred to as a ``metastable'' state. The manner in which the metastable state decays depends on the strength of the magnetic field and the system size; the ``thermodynamic spinodal'' is the transition between systems large enough to contain a single critical droplet and systems that are too small to do so, and the ``dynamic spinodal'' marks the transition between decay as a Poisson process to decay that is ``deterministic'', meaning the standard deviation of the lifetime of the metastable state is small compared with its mean value. However, in the hyperbolic plane, true metastability exists, and evidence shows that the thermodynamic spinodal and dynamic spinodal are numerically close to the true spinodal, the field below which the metastable state cannot decay through the nucleation and growth of droplets. This research was supported by NSF Grant OCI-1005117.
Spot size variation FCS in simulations of the 2D Ising model
NASA Astrophysics Data System (ADS)
Burns, Margaret C.; Nouri, Mariam; Veatch, Sarah L.
2016-06-01
Spot variation fluorescence correlation spectroscopy (svFCS) was developed to study the movement and organization of single molecules in plasma membranes. This experimental technique varies the size of an illumination area while measuring correlations in time using standard fluorescence correlation methods. Frequently, this data is interpreted using the assumption that correlation measurements reflect the dynamics of single molecule motions, and not motions of the average composition. Here, we explore how svFCS measurements report on the dynamics of components diffusing within simulations of a 2D Ising model with a conserved order parameter. Simulated correlation functions report on both the fast dynamics of single component mobility and the slower dynamics of the average composition. Over a range of simulation conditions, a conventional svFCS analysis suggests the presence of anomalous diffusion even though single molecule motions are nearly Brownian in these simulations. This misinterpretation is most significant when the surface density of the fluorescent label is elevated, therefore we suggest future measurements be made over a range of tracer densities. Some simulation conditions reproduce qualitative features of published svFCS experimental data. Overall, this work emphasizes the need to probe membranes using multiple complimentary experimental methodologies in order to draw conclusions regarding the nature of spatial and dynamical heterogeneity in these systems.
NASA Astrophysics Data System (ADS)
Zenine, N.; Boukraa, S.; Hassani, S.; Maillard, J.-M.
2005-10-01
We present a simple, but efficient, way to calculate connection matrices between sets of independent local solutions, defined at two neighbouring singular points, of Fuchsian differential equations of quite large orders, such as those found for the third and fourth contribution (χ(3) and χ(4)) to the magnetic susceptibility of the square lattice Ising model. We deduce all the critical behaviours of the solutions χ(3) and χ(4), as well as the asymptotic behaviour of the coefficients in the corresponding series expansions. We confirm that the newly found quadratic singularities of the Fuchsian ODE associated with χ(3) are not singularities of the particular solution χ(3) itself. We use the previous connection matrices to get the exact expressions of all the monodromy matrices of the Fuchsian differential equation for χ(3) (and χ(4)) expressed in the same basis of solutions. These monodromy matrices are the generators of the differential Galois group of the Fuchsian differential equations for χ(3) (and χ(4)), whose analysis is just sketched here. As far as the physics implications of the solutions are concerned, we find challenging qualitative differences when comparing the corrections to scaling for the full susceptibility χ at high temperature (respectively low temperature) and the first two terms χ(1) and χ(3) (respectively χ(2) and χ(4)).
NASA Astrophysics Data System (ADS)
Zenine, N.; Boukraa, S.; Hassani, S.; Maillard, J.-M.
2006-06-01
We first study the properties of the Fuchsian ordinary differential equations for the three and four-particle contributions χ(3) and χ(4) of the square lattice Ising model susceptibility. An analysis of some mathematical properties of these Fuchsian differential equations is sketched. For instance, we study the factorization properties of the corresponding linear differential operators, and consider the singularities of the three and four-particle contributions χ(3) and χ(4), versus the singularities of the associated Fuchsian ordinary differential equations, which actually exhibit new ''Landau-like'' singularities. We sketch the analysis of the corresponding differential Galois groups. In particular we provide a simple, but efficient, method to calculate the so-called ''connection matrices'' (between two neighboring singularities) and deduce the singular behaviors of χ(3) and χ(4). We provide a set of comments and speculations on the Fuchsian ordinary differential equations associated with the n-particle contributions χ(n) and address the problem of the apparent discrepancy between such a holonomic approach and some scaling results deduced from a Painlevé oriented approach.
Operator product expansion coefficients of the 3D Ising model with a trapping potential
NASA Astrophysics Data System (ADS)
Costagliola, Gianluca
2016-03-01
Recently the operator product expansion coefficients of the 3D Ising model universality class have been calculated by studying via Monte Carlo simulation the two-point functions perturbed from the critical point with a relevant field. We show that this method can be applied also when the perturbation is performed with a relevant field coupled to a nonuniform potential acting as a trap. This setting is described by the trap size scaling ansatz, which can be combined with the general framework of the conformal perturbation in order to write down the correlators ⟨σ (r )σ (0 )⟩, ⟨σ (r )ɛ (0 )⟩ and ⟨ɛ (r )ɛ (0 )⟩, from which the operator product expansion coefficients can be estimated. We find Cσɛ σ=1.051 (3 ), in agreement with the results already known in the literature, and Cɛɛ ɛ=1.32 (15 ), confirming and improving the previous estimate obtained in the uniform perturbation case.
Hysteresis in DNA compaction by Dps is described by an Ising model.
Vtyurina, Natalia N; Dulin, David; Docter, Margreet W; Meyer, Anne S; Dekker, Nynke H; Abbondanzieri, Elio A
2016-05-01
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
Nematic phase in the J1-J2 square-lattice Ising model in an external field
NASA Astrophysics Data System (ADS)
Guerrero, Alejandra I.; Stariolo, Daniel A.; Almarza, Noé G.
2015-05-01
The J1-J2 Ising model in the square lattice in the presence of an external field is studied by two approaches: the cluster variation method (CVM) and Monte Carlo simulations. The use of the CVM in the square approximation leads to the presence of a new equilibrium phase, not previously reported for this model: an Ising-nematic phase, which shows orientational order but not positional order, between the known stripes and disordered phases. Suitable order parameters are defined, and the phase diagram of the model is obtained. Monte Carlo simulations are in qualitative agreement with the CVM results, giving support to the presence of the new Ising-nematic phase. Phase diagrams in the temperature-external field plane are obtained for selected values of the parameter κ =J2/|J1| which measures the relative strength of the competing interactions. From the CVM in the square approximation we obtain a line of second order transitions between the disordered and nematic phases, while the nematic-stripes phase transitions are found to be of first order. The Monte Carlo results suggest a line of second order nematic-disordered phase transitions in agreement with the CVM results. Regarding the stripes-nematic transitions, the present Monte Carlo results are not precise enough to reach definite conclusions about the nature of the transitions.
Critical fluctuations in the one-dimensional Bak-Sneppen model
NASA Astrophysics Data System (ADS)
Qian, W. Y.; Yang, C. B.
2012-11-01
The critical fluctuation properties of fitness distribution in the one-dimensional Bak-Sneppen model are studied in terms of the normalized factorial moments, erraticity moments and the factorial correlators. For a fitness window below the gap intermittent behaviors are observed. The scaling exponent for the BS model is different from that in two dimensional Ising model for second order phase transition. There is no correlation between fluctuations in two windows separated by the critical gap.
Degenerate Ising model for atomistic simulation of crystal-melt interfaces
Schebarchov, D.; Schulze, T. P.; 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) lattices 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.
Degenerate Ising model for atomistic simulation of crystal-melt interfaces.
Schebarchov, D; Schulze, T P; 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) lattices 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. PMID:24559357
A Renormalization Group Study of the Ising Model on the Hierarchical Hanoi Networks
NASA Astrophysics Data System (ADS)
Brunson, Clifton Trent
Despite all the remarkable breakthroughs in the area of complex networks over the last two decades, there still lacks a complete and general understanding of effects that occur when long-range connections are present in a system. This thesis explores the Ising model using recursive hierarchical networks called Hanoi networks (HN) as a substrate. Hanoi networks are purely synthetic and are not found in nature, so it is important to establish and not lose sight of why they worth studying. In essence, we are not strictly interested in HNs themselves, but the generalized statements about phase transitions on complex networks that they provide via the renormalization group (RG). The RG framework on HNs is established in this study and the thermodynamic observables for statistical models are derived from it. Traditionally, the RG has given physicists insight into the critical exponents of a system or model, which leads to universal behavior; however, hyperbolic networks, like the ones currently under investigation, do not contain constant exponents and do not exhibit universality. Instead, it is found that the scaling exponents are functions of the temperature. We ultimately want to answer the questions: What is it about long-range connections that create a break in universal behavior and can complex networks be designed to produce predicted and intended effects in phase behavior? The current state of research is several years or perhaps decades away from fully comprehending the answers to these questions. The research presented here is motivated by these questions, and our contribution here is intended to show a generalized picture of phase transitions on networks.
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.
Generation of Control by SU(2) Reduction for the Anisotropic Ising Model
NASA Astrophysics Data System (ADS)
Delgado, F.
2016-03-01
Control of entanglement is fundamental in Quantum Information and Quantum Computation towards scalable spin-based quantum devices. For magnetic systems, Ising interaction with driven magnetic fields modifies entanglement properties of matter based quantum systems. This work presents a procedure for dynamics reduction on SU(2) subsystems using a non-local description. Some applications for Quantum Information are discussed.
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.
NASA Astrophysics Data System (ADS)
Fritsch, K.; Ehlers, G.; Rule, K. C.; Habicht, K.; Ramazanoglu, M.; Dabkowska, H. A.; Gaulin, B. D.
2015-11-01
The application of a magnetic field transverse to the easy axis, Ising direction in the quasi-two-dimensional kagome staircase magnet, Co3V2O8 , 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. At least one of the transitions to incommensurate phases at μ0Hc 1˜6.25 T and μ0Hc 2˜7 T is discontinuous, while the final quantum critical point at μ0Hc 3˜13 T is continuous.
Fritsch, Katharina; Ehlers, G.; Rule, K. C.; Habicht, Klaus; Ramazanoglu, Mehmet K.; Dabkowska, H. A.; Gaulin, Bruce D.
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, Co3V2O8, 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 μ0Hc1~6.25 T and μ0Hc2~7 T is discontinuous, while the final quantum critical point at μ0Hc3~13 T ismore » continuous.« less
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.
XY ring exchange model with frustrated Ising coupling on the triangular lattice
NASA Astrophysics Data System (ADS)
Owerre, S. A.
2016-07-01
We investigate the nature of a Z2-invariant XY ring-exchange interaction with a frustrated Ising coupling on the triangular lattice. Within the limits of pure XY ring-exchange interaction, we show that the classical ground state is degenerate resulting from the Z2-invariance of the Hamiltonian. Quantum fluctuations lift these classical degenerate ground states and produce an unusual state whose excitation spectrum exhibits a gapped maximum quadratic dispersion near k = 0 and vanishes at the midpoints of each side of the Brillouin zone. This result is in contrast to a gapless quadratic dispersion near k = 0 in the U(1)-invariant counterpart. We also study the effects of frustration when competing with a classically frustrated Ising interaction. We provide a glimpse into the possible quantum phases that could emerge. A comprehensive understanding of this Hamiltonian, however, cannot be elucidated analytically and requires an explicit numerical simulation.
LeVine, Michael V.; Weinstein, Harel
2015-01-01
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. PMID:26594108
A New Proof of the Sharpness of the Phase Transition for Bernoulli Percolation and the Ising Model
NASA Astrophysics Data System (ADS)
Duminil-Copin, Hugo; Tassion, Vincent
2016-04-01
We provide a new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model. The proof applies to infinite-range models on arbitrary locally finite transitive infinite graphs. For Bernoulli percolation, we prove finiteness of the susceptibility in the subcritical regime {β < β_c}, and the mean-field lower bound {{P}_β[0longleftrightarrow infty ]ge (β-β_c)/β} for {β > β_c}. For finite-range models, we also prove that for any {β < β_c}, the probability of an open path from the origin to distance n decays exponentially fast in n. For the Ising model, we prove finiteness of the susceptibility for {β < β_c}, and the mean-field lower bound {< σ_0rangle_β^+ge sqrt{(β^2-β_c^2)/β^2}} for {β > β_c}. For finite-range models, we also prove that the two-point correlation functions decay exponentially fast in the distance for {β < β_c}.
Rudnick, Joseph; Zandi, Roya; Shackell, Aviva; Abraham, Douglas
2010-10-01
Finite-size effects in certain critical systems can be understood as universal Casimir forces. Here, we compare the Casimir force for free, fixed, periodic, and antiperiodic boundary conditions in the exactly calculable case of the ferromagnetic Ising model in one and two dimensions. We employ a procedure which allows us to calculate the Casimir force with the aforementioned boundary conditions analytically in a transparent manner. Among other results, we find an attractive Casimir force for the case of periodic boundary conditions and a repulsive Casimir force in the antiperiodic case. PMID:21230249
Magnetic properties of the spin-3/2 Blume-Capel model on a hexagonal Ising nanowire
Kocakaplan, Y.; Ertaş, M.
2015-10-15
Magnetic properties, such as magnetizations, internal energy, specific heat, entropy, Helmholtz free energy, and phase diagrams of the spin-3/2 Blume-Capel model on a hexagonal Ising nanowire with core-shell structure are studied by using the effective-field theory with correlations. The hysteresis behaviors of the system are also investigated and the effects of Hamiltonian parameters on hysteresis behaviors are discussed in detail. The obtained results are compared with some theoretical results and a qualitatively good agreement is found.
Performance of Replica-Exchange Wang-Landau Sampling for the 2D Ising Model: A Brief Survey
Zhao, Yiwei; Cheung, Siu Wun; Li, Ying Wai; Eisenbach, Markus
2014-01-01
We report a brief performance study of the replica-exchange Wang-Landau algorithm, a recently proposed parallel realization of Wang-Landau sampling, using the 2D Ising model as a test case. The simulation time is found to scale inversely with the square root of the number of subwindows (and thus number of processors) used to span the global parameter space. We also investigate the time profiles for random walkers in dierent subwindows to complete iterations, which will aid the development of and adaptive load-balancing scheme.
NASA Astrophysics Data System (ADS)
Barton, J. P.; Cocco, S.; De Leonardis, E.; Monasson, R.
2014-07-01
The mean-field (MF) approximation offers a simple, fast way to infer direct interactions between elements in a network of correlated variables, a common, computationally challenging problem with practical applications in fields ranging from physics and biology to the social sciences. However, MF methods achieve their best performance with strong regularization, well beyond Bayesian expectations, an empirical fact that is poorly understood. In this work, we study the influence of pseudocount and L2-norm regularization schemes on the quality of inferred Ising or Potts interaction networks from correlation data within the MF approximation. We argue, based on the analysis of small systems, that the optimal value of the regularization strength remains finite even if the sampling noise tends to zero, in order to correct for systematic biases introduced by the MF approximation. Our claim is corroborated by extensive numerical studies of diverse model systems and by the analytical study of the m-component spin model for large but finite m. Additionally, we find that pseudocount regularization is robust against sampling noise and often outperforms L2-norm regularization, particularly when the underlying network of interactions is strongly heterogeneous. Much better performances are generally obtained for the Ising model than for the Potts model, for which only couplings incoming onto medium-frequency symbols are reliably inferred.
Magnetic and magnetocaloric properties of quasi-one-dimensional Ising spin chain CoV2O6
NASA Astrophysics Data System (ADS)
Nandi, M.; Mandal, P.
2016-04-01
We have investigated the magnetic and magnetocaloric properties of antiferromagnetic Ising spin chain CoV2O6 by magnetization and heat capacity measurements. Both monoclinic α-CoV2O6 and triclinic γ-CoV2O6 exhibit field-induced metamagnetic transitions from antiferromagnetic to ferromagnetic state via an intermediate ferrimagnetic state with 1/3 magnetization plateau. Due to the field-induced metamagnetic transitions, these systems show large conventional as well as inverse magnetocaloric effects. In α-CoV2O6, we observe field-induced complex magnetic phases and multiple magnetization plateaus below 6 K when the field is applied along c axis. Several critical temperatures and fields have been identified from the temperature and field dependence of magnetization, magnetic entropy change, and heat capacity to construct the H-T phase diagram. As compared to α-CoV2O6, γ-CoV2O6 displays a relatively simple magnetic phase diagram. Due to the large magnetic entropy change and adiabatic temperature change at low or moderate applied magnetic field, γ-CoV2O6 may be considered as a magnetic refrigerant in the low-temperature region below 20 K.
Strečka, Jozef; Ekiz, Cesur
2015-05-01
The geometrically frustrated spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices is exactly solved by combining the generalized star-triangle transformation with the method of exact recursion relations. The ground-state and finite-temperature phase diagrams are rigorously calculated along with both sublattice magnetizations of the Ising and Heisenberg spins. It is evidenced that the Ising-Heisenberg model on triangulated Husimi lattices with two or three interconnected triangles-in-triangles units displays in a highly frustrated region a quantum disorder irrespective of temperature, whereas the same model on triangulated Husimi lattices with a greater connectivity of triangles-in-triangles units exhibits at low enough temperatures an outstanding quantum order due to the order-by-disorder mechanism. The quantum reduction of both sublattice magnetizations in the peculiar quantum ordered state gradually diminishes upon increasing the coordination number of the underlying Husimi lattice. PMID:26066155
Translation-invariant p-adic quasi-Gibbs measures for the Ising-Vannimenus model on a Cayley tree
NASA Astrophysics Data System (ADS)
Mukhamedov, F. M.; Saburov, M. Kh.; Khakimov, O. Kh.
2016-04-01
We consider the p-adic Ising-Vannimenus model on the Cayley tree of order k = 2. This model contains nearest-neighbor and next-nearest-neighbor interactions. We investigate the model using a new approach based on measure theory ( in the p-adic sense) and describe all translation-invariant p-adic quasi-Gibbs measures associated with the model. As a consequence, we can prove that a phase transition exists in the model. Here, "phase transition" means that there exist at least two nontrivial p-adic quasi-Gibbs measures such that one is bounded and the other is unbounded. The methods used are inapplicable in the real case.
NASA Astrophysics Data System (ADS)
Jiménez, Andrea
2014-02-01
We study the unexpected asymptotic behavior of the degeneracy of the first few energy levels in the antiferromagnetic Ising model on triangulations of closed Riemann surfaces. There are strong mathematical and physical reasons to expect that the number of ground states (i.e., degeneracy) of the antiferromagnetic Ising model on the triangulations of a fixed closed Riemann surface is exponential in the number of vertices. In the set of plane triangulations, the degeneracy equals the number of perfect matchings of the geometric duals, and thus it is exponential by a recent result of Chudnovsky and Seymour. From the physics point of view, antiferromagnetic triangulations are geometrically frustrated systems, and in such systems exponential degeneracy is predicted. We present results that contradict these predictions. We prove that for each closed Riemann surface S of positive genus, there are sequences of triangulations of S with exactly one ground state. One possible explanation of this phenomenon is that exponential degeneracy would be found in the excited states with energy close to the ground state energy. However, as our second result, we show the existence of a sequence of triangulations of a closed Riemann surface of genus 10 with exactly one ground state such that the degeneracy of each of the 1st, 2nd, 3rd and 4th excited energy levels belongs to O( n), O( n 2), O( n 3) and O( n 4), respectively.
Star-triangle relation for a three-dimensional model
Bazhanov, V.V. Institute for High Eenrgy Physics, Protvino, Moscow Region ); Baxter, R.J. Australian National Univ., Canberra )
1993-06-01
The solvable sl(n)-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising-type model on the body-centered cubic lattice with two- and three-spin interactions. The corresponding local Boltzmann weights obey a number of simple relations, including a restricted star-triangle relation, which is a modified version of the well-known star-triangle relation appearing in two-dimensional models. It is shown that these relations lead to remarkable symmetry properties of the Boltzmann weight function of an elementary cube of the lattice, related to the spatial symmetry group of the cubic lattice. These symmetry properties allow one to prove the commutativity of the row-to-row transfer matrices, bypassing the tetrahedron relation. The partition function per site for the infinite lattice is calculated exactly. 20 refs., 4 figs.
S=½ Ising Behavior in the Two-dimensional Molecular Magnet Fe(NCS)_{2}(pyrazine)_{2}
Bordallo, H. N.; Chapon, L. C.; Manson, Jamie L; Hernandez-Velasco, J.; Ravot, D.; Reiff, W. M.; Argyriou, D. N.
2004-01-01
The magnetic ordering and critical behavior of antiferromagnetic Fe(NCS){sub 2}(pyrazine){sub 2} has been studied by neutron powder diffraction (NPD), inelastic neutron scattering (INS), Moessbauer spectroscopy, and magnetic measurements. The system can be regarded as a two-dimensional (2D) antiferromagnet even in the ordered phase, given that long-range magnetic ordering between the layers simply follows a necessary consequence of the establishment of long-range ordering within the planes. The INS data, which were taken on a cold neutron time-of-flight spectrometer, reveals that when the temperature is lowered towards T{sub N}, the correlation length within the 2D layers increases and ultimately crosses over from two- to three-dimensional (3D) behavior. Indeed, 3D long-range antiferromagnetic order, associated with a propagation vector [1,0,1/4+{epsilon}], is observed in the NPD data below 6.8 K. Furthermore, in agreement with the behavior of both {chi}(T) and C{sub m}(T) data, the order parameter follows the exact Osanger solution for a 2D S = 1/2, Ising system.
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.
Trobo, Marta L; Albano, Ezequiel V
2016-03-31
Fixed vacancies (non-magnetic impurities) are placed along the centre of Ising strips in order to study the wetting behaviour in this confined system, by means of numerical simulations analysed with the aid of finite size scaling and thermodynamic integration methods. By considering strips of size L × M (L < M) where short-range competitive surface fields (H(s)) act along the M-direction, we observe localization-delocalization transitions of the interface between magnetic domains of different orientation (driven by the corresponding surface fields), which are the precursors of the wetting transitions that occur in the thermodynamic limit. By placing vacancies or equivalently non-magnetic impurities along the centre of the sample, we found that for low vacancy densities the wetting transitions are of second order, while by increasing the concentration of vacancies the transitions become of first order. Second- and first-order lines meet in tricritical wetting points (H(tric)(SW), T(tric)(W)), where H(tric)(SW) and T(Tric)(W) are the magnitude of the surface field and the temperature, respectively. In the phase diagram, tricritical points shift from the high temperature and weak surface field regime at large vacancy densities to the T --> 0, H(tric)(SW) --> 1 limit for low vacancy densities. By comparing the locations of the tricritical points with those corresponding to the case of mobile impurities, we conclude that in order to observe similar effects, in the latter the required density of impurities is much smaller (e.g. by a factor 3-5). Furthermore, a proper density of non magnetic impurities placed along the centre of a strip can effectively pin rather flat magnetic interfaces for suitable values of the competing surface fields and temperature. PMID:26910650
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.
NASA Astrophysics Data System (ADS)
Jurčišinová, E.; Jurčišin, M.
2016-02-01
We investigate the second order phase transitions of the ferromagnetic spin-1 Ising model on pure Husimi lattices built up from elementary squares with arbitrary values of the coordination number. It is shown that the critical temperatures of the second order phase transitions are driven by a single equation simultaneously on all such lattices. It is also shown that for arbitrary given value of the coordination number this equation is equivalent to the corresponding polynomial equation. The explicit form of these polynomial equations is present for the lattices with the coordination numbers z = 4 , 6, and 8. It is proven that, at least for the small values of the coordination number, the positions of the critical temperatures are uniquely determined. In addition, it is shown that the properties of all phases of the model are also driven by the corresponding single equations simultaneously on all pure Husimi lattices built up from elementary squares. The spontaneous magnetization of the model is investigated in detail.
NASA Astrophysics Data System (ADS)
Chen, J.; Zhuo, W. Z.; Qin, M. H.; Dong, S.; Zeng, M.; Lu, X. B.; Gao, X. S.; Liu, J.-M.
2016-09-01
In this work, we study the magnetization behaviors of the classical Ising model on the triangular lattice using Monte Carlo simulations, and pay particular attention to the effect of further-neighbor interactions. Several fascinating spin states are identified to be stabilized in certain magnetic field regions, respectively, resulting in the magnetization plateaus at 2/3, 5/7, 7/9 and 5/6 of the saturation magnetization M S, in addition to the well-known plateaus at 0, 1/3 and 1/2 of M S. The stabilization of these interesting orders can be understood as the consequence of the competition between Zeeman energy and exchange energy.
Chen, J; Zhuo, W Z; Qin, M H; Dong, S; Zeng, M; Lu, X B; Gao, X S; Liu, J-M
2016-09-01
In this work, we study the magnetization behaviors of the classical Ising model on the triangular lattice using Monte Carlo simulations, and pay particular attention to the effect of further-neighbor interactions. Several fascinating spin states are identified to be stabilized in certain magnetic field regions, respectively, resulting in the magnetization plateaus at 2/3, 5/7, 7/9 and 5/6 of the saturation magnetization M S, in addition to the well-known plateaus at 0, 1/3 and 1/2 of M S. The stabilization of these interesting orders can be understood as the consequence of the competition between Zeeman energy and exchange energy. PMID:27356040
Quantum Monte Carlo study of long-range transverse-field Ising models on the triangular lattice
NASA Astrophysics Data System (ADS)
Humeniuk, Stephan
2016-03-01
Motivated by recent experiments with a Penning ion trap quantum simulator, we perform numerically exact Stochastic Series Expansion quantum Monte Carlo simulations of long-range transverse-field Ising models on a triangular lattice for different decay powers α of the interactions. The phase boundary for the ferromagnet is obtained as a function of α . For antiferromagnetic interactions, there is strong indication that the transverse field stabilizes a clock ordered phase with sublattice magnetization (M ,-M/2 ,-M/2 ) with unsaturated M <1 in a process known as "order by disorder" similar to the nearest-neighbor antiferromagnet on the triangular lattice. Connecting the known limiting cases of nearest-neighbor and infinite-range interactions, a semiquantitative phase diagram is obtained. Magnetization curves for the ferromagnet for experimentally relevant system sizes and with open boundary conditions are presented.
Topological phases of shaken quantum Ising lattices
NASA Astrophysics Data System (ADS)
Fernández-Lorenzo, Samuel; José García-Ripoll, Juan; Porras, Diego
2016-02-01
The quantum compass model consists of a two-dimensional square spin lattice where the orientation of the spin-spin interactions depends on the spatial direction of the bonds. It has remarkable symmetry properties and the ground state shows topological degeneracy. The implementation of the quantum compass model in quantum simulation setups like ultracold atoms and trapped ions is far from trivial, since spin interactions in those systems typically are independent of the spatial direction. Ising spin interactions, on the contrary, can be induced and controlled in atomic setups with state-of-the art experimental techniques. In this work, we show how the quantum compass model on a rectangular lattice can be simulated by the use of the photon-assisted tunneling induced by periodic drivings on a quantum Ising spin model. We describe a procedure to adiabatically prepare one of the doubly degenerate ground states of this model by adiabatically ramping down a transverse magnetic field, with surprising differences depending on the parity of the lattice size. Exact diagonalizations confirm the validity of this approach for small lattices. Specific implementations of this scheme are presented with ultracold atoms in optical lattices in the Mott insulator regime, as well as with Rydberg atoms.
Entanglement detection in the mixed-spin Ising-X Y model
NASA Astrophysics Data System (ADS)
Hamid Arian, Zad
2016-03-01
In the present work, we initially verify anisotropy effect on the heat capacity of a mixed-three-spin (1/2,1,1/2) system (where spins (1/2,1/2) have XY interaction and spins (1,1/2) have Ising interaction together) at finite temperatures, then, the pairwise entanglement for spins (1/2,1/2), by means of negativity (as a measure of entanglement) as a function of the temperature T, homogeneous magnetic field B, and anisotropy parameter γ is investigated. In addition, we show that one can find magnetic phase transition points for the spins (1/2,1/2) at finite temperatures and understand properly their behavior with respect to the magnetic field and the anisotropy parameter, via the negativity function. An interval of the magnetic field from the negativity diagram of the spins (1/2,1/2) is presented in which quantum phase transition occurs for the tripartite mixed-three-spin system. Finally, some new interesting entanglement witnesses are introduced by using non-degenerate perturbation theory for the mixed-three-spin system.
Flat-histogram Monte Carlo in the Classical Antiferromagnetic Ising Model
NASA Astrophysics Data System (ADS)
Brown, G.; Rikvold, P. A.; Nicholson, D. M.; Odbadrakh, Kh.; Yin, J.-Q.; Eisenbach, M.; Miyashita, S.
2014-03-01
Flat-histogram Monte Carlo methods, such as Wang-Landau and multicanonical sampling, are extremely useful in numerical studies of frustrated magnetic systems. Numerical tools such as windowing and discrete histograms introduce discontinuities along the continuous energy variable, which in turn introduce artifacts into the calculated density of states. We demonstrate these effects and introduce practical solutions, including ``guard regions'' with biased walks for windowing and analytic representations for histograms. The classical Ising antiferromagnet supplemented by a mean-field interaction is considered. In zero field, the allowed energies are discrete and the artifacts can be avoided in small systems by not binning. For large systems, or cases where non-zero fields are used to break the degeneracy between local energy minima, the energy becomes continuous and these artifacts must be taken into account. Work performed at ORNL, managed by UT-Batelle for the US DOE; sponsored by Div of Mat Sci & Eng, Office of BES; used resources of Oak Ridge Leadership Computing Facility at ORNL, supported by Office of Science Contract DE-AC05-00OR22725.
Inverse Ising inference with correlated samples
NASA Astrophysics Data System (ADS)
Obermayer, Benedikt; Levine, Erel
2014-12-01
Correlations between two variables of a high-dimensional system can be indicative of an underlying interaction, but can also result from indirect effects. Inverse Ising inference is a method to distinguish one from the other. Essentially, the parameters of the least constrained statistical model are learned from the observed correlations such that direct interactions can be separated from indirect correlations. Among many other applications, this approach has been helpful for protein structure prediction, because residues which interact in the 3D structure often show correlated substitutions in a multiple sequence alignment. In this context, samples used for inference are not independent but share an evolutionary history on a phylogenetic tree. Here, we discuss the effects of correlations between samples on global inference. Such correlations could arise due to phylogeny but also via other slow dynamical processes. We present a simple analytical model to address the resulting inference biases, and develop an exact method accounting for background correlations in alignment data by combining phylogenetic modeling with an adaptive cluster expansion algorithm. We find that popular reweighting schemes are only marginally effective at removing phylogenetic bias, suggest a rescaling strategy that yields better results, and provide evidence that our conclusions carry over to the frequently used mean-field approach to the inverse Ising problem.
Four-particle decay of the Bethe-Salpeter kernel in the high-temperature Ising model
NASA Astrophysics Data System (ADS)
Auil, F.
2002-12-01
In this article we study the four-particle decay of the Bethe-Salpeter (B-S) kernel for the high-temperature Ising model. We use the hyperplane decoupling method [T. Spencer, Commun. Math. Phys. 44, 143 (1975); R. S. Schor, Nucl. Phys. B 222, 71 (1983)] to prove exponential decay in a set of variables particularly adapted to the methods of Spencer and Zirilli [Commun. Math. Phys. 49, 1 (1976)] for the analysis of scattering and bound states in QFT, transcribed to lattice theories by Auil and Barata [Ann. Henri Poincare 2, 1065 (2001)]. We study arbitrary derivatives of the general n-point correlation functions with respect to the interpolating variables, and we are able to obtain, in some cases, information about the third derivatives of the B-S kernel. As a later consequence, we have two-body asymptotic completeness for the (massive) Euclidean lattice field theory implemented by this model. This allows us to analyze the Ornstein-Zernike behavior of four-point functions, related to the specific heat of the model.
Liu, R M; Zhuo, W Z; Dong, S; Lu, X B; Gao, X S; Qin, M H; Liu, J-M
2016-03-01
In this work, we investigate the phase transitions and critical behaviors of the frustrated J(1)-J(2)-J(3) Ising model on the square lattice using Monte Carlo simulations, and particular attention goes to the effect of the second-next-nearest-neighbor interaction J(3) on the phase transition from a disordered state to the single stripe antiferromagnetic state. A continuous Ashkin-Teller-like transition behavior in a certain range of J(3) is identified, while the four-state Potts-critical end point [J(3)/J(1)](C) is estimated based on the analytic method reported in earlier work [Jin, Sen, and Sandvik, Phys. Rev. Lett. 108, 045702 (2012)]. It is suggested that the interaction J(3) can tune the transition temperature and in turn modulate the critical behaviors of the frustrated model. Furthermore, it is revealed that an antiferromagnetic J(3) can stabilize the staggered dimer state via a phase transition of strong first-order character. PMID:27078299
NASA Astrophysics Data System (ADS)
Maruo, Daiki; Utsunomiya, Shoko; Yamamoto, Yoshihisa
2016-08-01
We present the quantum theory of coherent Ising machines based on networks of degenerate optical parametric oscillators (DOPOs). In a simple model consisting of two coupled DOPOs, both positive-P representation and truncated Wigner representation predict quantum correlation and inseparability between the two DOPOs in spite of the open-dissipative nature of the system. Here, we apply the truncated Wigner representation method to coherent Ising machines with thermal, vacuum, and squeezed reservoir fields. We find that the probability of finding the ground state of a one-dimensional Ising model increases substantially as a result of reducing excess thermal noise and squeezing the incident vacuum fluctuation on the out-coupling port.
NASA Astrophysics Data System (ADS)
Kohring, G. A.; Stauffer, D.
Geometric parallelization was tested on the Intel Hypercube with 32 MIMD processors of 1860 type, each with 16 Mbytes of distributed memory. We applied it to Ising models in two and three dimensions as well as to neural networks and two-dimensional hydrodynamic cellular automata. For system sizes suited to this machine, up to 60960*60960 and 1410*1410*1408 Ising spins, we found nearly hundred percent parallel efficiency in spite of the needed inter-processor communications. For small systems, the observed deviations from full efficiency were compared with the scaling concepts of Heermann and Burkitt and of Jakobs and Gerling. For Ising models, we determined the Glauber kinetic exponent z≃2.18 in two dimensions and confirmed the stretched exponential relaxation of the magnetization towards the spontaneous magnetization below Tc. For three dimensions we found z≃2.09 and simple exponential relaxation.
NASA Astrophysics Data System (ADS)
Sampaio Filho, C. I. N.; dos Santos, T. B.; Moreira, A. A.; Moreira, F. G. B.; Andrade, J. S.
2016-05-01
We study through Monte Carlo simulations and finite-size scaling analysis the nonequilibrium phase transitions of the majority-vote model taking place on spatially embedded networks. These structures are built from an underlying regular lattice over which directed long-range connections are randomly added according to the probability Pi j˜r-α , where ri j is the Manhattan distance between nodes i and j , and the exponent α is a controlling parameter [J. M. Kleinberg, Nature (London) 406, 845 (2000), 10.1038/35022643]. Our results show that the collective behavior of this system exhibits a continuous order-disorder phase transition at a critical parameter, which is a decreasing function of the exponent α . Precisely, considering the scaling functions and the critical exponents calculated, we conclude that the system undergoes a crossover among distinct universality classes. For α ≤3 the critical behavior is described by mean-field exponents, while for α ≥4 it belongs to the Ising universality class. Finally, in the region where the crossover occurs, 3 <α <4 , the critical exponents are dependent on α .
NASA Astrophysics Data System (ADS)
Martinelli, Fabio; Toninelli, Fabio Lucio
2010-05-01
We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature β and random boundary conditions τ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to + (equal to -). For β large enough we show that for any {\\varepsilon >0 } there exists {c=c(β,\\varepsilon)} such that the corresponding mixing time T mix satisfies {lim_{Ltoinfty} {P}left(T_mixge exp({cL^\\varepsilon})right) =0}. In the non-random case τ ≡ + (or τ ≡ -), this implies that {T_mixle exp({cL^\\varepsilon})}. The same bound holds when the boundary conditions are all + on three sides and all - on the remaining one. The result, although still very far from the expected Lifshitz behavior T mix = O( L 2), considerably improves upon the previous known estimates of the form {T_mixle exp({c L^{frac 12 + \\varepsilon}})}. The techniques are based on induction over length scales, combined with a judicious use of the so-called “censoring inequality” of Y. Peres and P. Winkler, which in a sense allows us to guide the dynamics to its equilibrium measure.
NASA Astrophysics Data System (ADS)
Deviren, Şeyma Akkaya; Deviren, Bayram
2016-03-01
The dynamic phase transitions and dynamic phase diagrams are studied, within a mean-field approach, in the kinetic Ising model on the Shastry-Sutherland lattice under the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. The time-dependence behavior of order parameters and the behavior of average order parameters in a period, which is also called the dynamic order parameters, as a function of temperature, are investigated. Temperature dependence of the dynamic magnetizations, hysteresis loop areas and correlations are investigated in order to characterize the nature (first- or second-order) of the dynamic phase transitions as well as to obtain the dynamic phase transition temperatures. We present the dynamic phase diagrams in the magnetic field amplitude and temperature plane. The phase diagrams exhibit a dynamic tricritical point and reentrant phenomena. The phase diagrams also contain paramagnetic (P), Néel (N), Collinear (C) phases, two coexistence or mixed regions, (N+C) and (N+P), which strongly depend on interaction parameters.
NASA Astrophysics Data System (ADS)
Al-Shakran, Mohammad; Kibler, Ludwig A.; Jacob, Timo; Ibach, Harald; Beltramo, Guillermo L.; Giesen, Margret
2016-09-01
This is Part I of two closely related papers, where we show that the specific adsorption of anions leads to a failure of the nearest-neighbor Ising model to describe island perimeter curvatures on Au(100) electrodes in dilute KBr, HCl and H2SO4 electrolytes and the therewith derived step diffusivity vs. step orientation. This result has major consequences for theoretical studies aiming at the understanding of growth, diffusion and degradation phenomena. Part I focuses on the experimental data. As shown theoretically in detail in Part II (doi:10.1016/j.susc.2016.03.022), a set of nearest-neighbor and next-nearest-neighbor interaction energies (ɛNN, ɛNNN) can uniquely be derived from the diffusivity of steps along <100> and <110>. We find strong repulsive next-nearest neighbor (NNN) interaction in KBr and HCl, whereas NNN interaction is negligibly for H2SO4. The NNN repulsive interaction energy ɛNNN therefore correlates positively with the Gibbs adsorption energy of the anions. We find furthermore that ɛNNN increases with increasing Br- and Cl- coverage. The results for ɛNN and ɛNNN are quantitatively consistent with the coverage dependence of the step line tension. We thereby establish a sound experimental base for theoretical studies on the energetics of steps in the presence of specific adsorption.
Dimensional models of personality disorder
WIDIGER, THOMAS A
2007-01-01
There is little doubt that someday the classification of personality disorder will be dimensional. The failures of the categorical model are so many and are so well established that it is difficult to imagine that this model will ultimately survive. This paper provides a brief discussion of the major alternative proposals for a dimensional classification of personality disorder. It is possible that the authors of a future edition of a psychiatric diagnostic manual will simply choose one of these alternative proposals. However, the ideal solution might be to develop a common, integrative representation including the important contributions of each of the models. PMID:18235857
NASA Astrophysics Data System (ADS)
Yu, Rong; Si, Qimiao
2015-09-01
Motivated by the properties of the iron chalcogenides, we study the phase diagram of a generalized Heisenberg model with frustrated bilinear-biquadratic interactions on a square lattice. We identify zero-temperature phases with antiferroquadrupolar and Ising-nematic orders. The effects of quantum fluctuations and interlayer couplings are analyzed. We propose the Ising-nematic order as underlying the structural phase transition observed in the normal state of FeSe, and discuss the role of the Goldstone modes of the antiferroquadrupolar order for the dipolar magnetic fluctuations in this system. Our results provide a considerably broadened perspective on the overall magnetic phase diagram of the iron chalcogenides and pnictides, and are amenable to tests by new experiments.
Yu, Rong; Si, Qimiao
2015-09-11
Motivated by the properties of the iron chalcogenides, we study the phase diagram of a generalized Heisenberg model with frustrated bilinear-biquadratic interactions on a square lattice. We identify zero-temperature phases with antiferroquadrupolar and Ising-nematic orders. The effects of quantum fluctuations and interlayer couplings are analyzed. We propose the Ising-nematic order as underlying the structural phase transition observed in the normal state of FeSe, and discuss the role of the Goldstone modes of the antiferroquadrupolar order for the dipolar magnetic fluctuations in this system. Our results provide a considerably broadened perspective on the overall magnetic phase diagram of the iron chalcogenides and pnictides, and are amenable to tests by new experiments. PMID:26406842
NASA Astrophysics Data System (ADS)
Kobayashi, S.; Mitsuda, S.; Ishikawa, M.; Miyatani, K.; Kohn, K.
1999-08-01
The formation of three-dimensional magnetic ordering has been studied on a quasi-one-dimensional magnet CoNb2O6 by mean-field calculations as well as neutron scattering measurements down to T=1.5 K under magnetic fields up to H∥c~600 Oe. Measurements of a deviation of the magnetic Bragg scattering function from the delta function in the ordered state reveal a surprisingly rich variety of the magnetic formation arising from an isosceles triangular arrangement of the magnetic chain with competing interchain interactions in the a-b plane. The competing interactions result in quasidegenerate ground states with different propagation wave numbers along the b* direction in the sinusoidally amplitude-modulated incommensurate magnetic (IC) phase. Our mean-field calculations qualitatively reproduce the complicated H∥c-T magnetic phase diagram and give evidence for a high degeneracy of ground states by calculating the H∥c-T dependence of the free energy curve in the propagation wave number space. In addition, a partial cancellation of the exchange field at the apex site from the base sites on the isosceles triangular lattice leads to a quasi-long-range ordering along the a axis in both IC and antiferromagnetic states where the correlation length along the a axis depends on the propagation wave number along the b* direction.
NASA Astrophysics Data System (ADS)
Eising, G.; Kooi, B. J.
2012-06-01
Growth and decay of clusters at temperatures below Tc have been studied for a two-dimensional Ising model for both square and triangular lattices using Monte Carlo (MC) simulations and the enumeration of lattice animals. For the lattice animals, all unique cluster configurations with their internal bonds were identified up to 25 spins for the triangular lattice and up to 29 spins for the square lattice. From these configurations, the critical cluster sizes for nucleation have been determined based on two (thermodynamic) definitions. From the Monte Carlo simulations, the critical cluster size is also obtained by studying the decay and growth of inserted, most compact clusters of different sizes. A good agreement is found between the results from the MC simulations and one of the definitions of critical size used for the lattice animals at temperatures T > ˜0.4 Tc for the square lattice and T > ˜0.2 Tc for the triangular lattice (for the range of external fields H considered). At low temperatures (T ≈ 0.2 Tc for the square lattice and T ≈ 0.1 Tc for the triangular lattice), magic numbers are found in the size distributions during the MC simulations. However, these numbers are not present in the critical cluster sizes based on the MC simulations, as they are present for the lattice animal data. In order to achieve these magic numbers in the critical cluster sizes based on the MC simulation, the temperature has to be reduced further to T ≈ 0.15 Tc for the square lattice. The observed evolution of magic numbers as a function of temperature is rationalized in the present work.
Numerical study of the spin-glass transition in a dilute Ising model on a triangular lattice
NASA Astrophysics Data System (ADS)
Andérico, Carmen Z.; Fernández, Julio F.; Streit, Thomas S. J.
1982-10-01
We study an Ising model with nearest-neighbor antiferromagnetic interactions. It is placed on a triangular lattice, where each site is occupied by a spin with x probability. There is no applied magnetic field. Randomness and frustration, two essential ingredients of spin-glasses, are present in this model. We study its critical properties here. The entropy is obtained by a transfer-matrix calculation as a function of x at low temperature (T=0.3JkB) for systems on a lattice of 10 × 20 sites. A fairly shallow minimum appears near x~=0.9, which suggests that this case is the one most likely to show a transition into an ordered state at low temperature. We study the cases x=1, 0.9, and 0.74, which is about half-way to the critical percolation. We simulate systems on lattices of 50 × 50 sites and 30 × 30 sites by the Monte Carlo method. The specific heat has a broad maximum at T~=0.9 for x=0.74 and 0.9. χSG, defined by χSG=N-1 i,j<σiσj>2, and the relaxation time (τ) are obtained for T>=0.6JkB. Both quantities, τ and χSG, turn out to be proportional to exp[A(T-T0)c] and 0<=T0<~0.4 a fit with T0=0 yields c~1 for x=1 but c~2 for x=0.74 and 0.9.
Functional scale-free networks in the two-dimensional Abelian sandpile model
NASA Astrophysics Data System (ADS)
Zarepour, M.; Niry, M. D.; Valizadeh, A.
2015-07-01
Recently, the similarity of the functional network of the brain and the Ising model was investigated by Chialvo [Nat. Phys. 6, 744 (2010), 10.1038/nphys1803]. This similarity supports the idea that the brain is a self-organized critical system. In this study we derive a functional network of the two-dimensional Bak-Tang-Wiesenfeld sandpile model as a self-organized critical model, and compare its characteristics with those of the functional network of the brain, obtained from functional magnetic resonance imaging.
Persistence in a Random Bond Ising Model of Socio-Econo Dynamics
NASA Astrophysics Data System (ADS)
Jain, S.; Yamano, T.
We study the persistence phenomenon in a socio-econo dynamics model using computer simulations at a finite temperature on hypercubic lattices in dimensions up to five. The model includes a "social" local field which contains the magnetization at time t. The nearest neighbour quenched interactions are drawn from a binary distribution which is a function of the bond concentration, p. The decay of the persistence probability in the model depends on both the spatial dimension and p. We find no evidence of "blocking" in this model. We also discuss the implications of our results for possible applications in the social and economic fields. It is suggested that the absence, or otherwise, of blocking could be used as a criterion to decide on the validity of a given model in different scenarios.
Large-scale Ising spin network based on degenerate optical parametric oscillators
NASA Astrophysics Data System (ADS)
Inagaki, Takahiro; Inaba, Kensuke; Hamerly, Ryan; Inoue, Kyo; Yamamoto, Yoshihisa; Takesue, Hiroki
2016-06-01
Solving combinatorial optimization problems is becoming increasingly important in modern society, where the analysis and optimization of unprecedentedly complex systems are required. Many such problems can be mapped onto the ground-state-search problem of the Ising Hamiltonian, and simulating the Ising spins with physical systems is now emerging as a promising approach for tackling such problems. Here, we report a large-scale network of artificial spins based on degenerate optical parametric oscillators (DOPOs), paving the way towards a photonic Ising machine capable of solving difficult combinatorial optimization problems. We generate >10,000 time-division-multiplexed DOPOs using dual-pump four-wave mixing in a highly nonlinear fibre placed in a cavity. Using those DOPOs, a one-dimensional Ising model is simulated by introducing nearest-neighbour optical coupling. We observe the formation of spin domains and find that the domain size diverges near the DOPO threshold, which suggests that the DOPO network can simulate the behaviour of low-temperature Ising spins.
Quantum Critical Behavior of the Bose-Fermi Kondo Model with Ising Anisotropy
NASA Astrophysics Data System (ADS)
Park, Tae-Ho
2005-03-01
The existence of a continous quantum phase transition of the Bose-Fermi Kondo Model (BFKM) with a self-consistently determined bosonic bath has been demonstrated within the Extended Dynamical Mean Field Approach to the anisotropic Kondo lattice model and φ/T-scaling near the quantum critical point(QCP)was found[1,2]. We study the quantum critical properties of the anisotropic BFKM with specified bath spectral function, where the spectrum of the bosonic bath vanishes in a power-law fashion with exponent γ for small frequencies. Motivated by very recent results that the quantum to classical mapping for a related class of models fails[3,4]. We determine the critical local susceptibility using both the classical and quantum Monte Carlo approaches of Ref.5. Our results cover several values of γ below and above the upper critical dimension of the classical model for temperatures down to 1% of the bare Kondo scale. [1]D. Grempel and Q. Si, Phys. Rev. Lett. 91, 026402 (2003). [2]J.Zhu, D. Grempel, and Q. Si, Phys. Rev. Lett. 91, 156404 (2003). [3]L. Zhu, S. Kirchner, Q. Si nad A. Georges, Phys. Rev. Lett. in press (cond-mat/0406293). [4]M. Vojta, N. Tong, and R. Bulla, cond-mat/0410132. [5]D. Grempel and M. Rozenberg, Phys. Rev. B 60, 4702 (1999).
Murtazaev, A. K.; Ramazanov, M. K.; Kassan-Ogly, F. A.; Kurbanova, D. R.
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-based model of opinion formation in a complex network of interpersonal interactions
NASA Astrophysics Data System (ADS)
Grabowski, A.; Kosiński, R. A.
2006-03-01
In our work the process of opinion formation in the human population, treated as a scale-free network, is modeled and investigated numerically. The individuals (nodes of the network) are characterized by their authorities, which influence the interpersonal interactions in the population. Hierarchical, two-level structures of interpersonal interactions and spatial localization of individuals are taken into account. The effect of the mass media, modeled as an external stimulation acting on the social network, on the process of opinion formation is investigated. It was found that in the time evolution of opinions of individuals critical phenomena occur. The first one is observed in the critical temperature of the system TC and is connected with the situation in the community, which may be described by such quantifiers as the economic status of people, unemployment or crime wave. Another critical phenomenon is connected with the influence of mass media on the population. As results from our computations, under certain circumstances the mass media can provoke critical rebuilding of opinions in the population.
Thermodynamics with long-range interactions: from Ising models to black holes.
Oppenheim, Jonathan
2003-07-01
Methods are presented which enables one to analyze the thermodynamics of systems with long-range interactions. Generically, such systems have entropies which are nonextensive (do not scale with the size of the system). We show how to calculate the degree of nonextensivity for such a system. We find that a system interacting with a heat reservoir is in a probability distribution of canonical ensembles. The system still possesses a parameter akin to a global temperature, which is constant throughout the substance. There is also a useful quantity which acts like a local temperatures and it varies throughout the substance. These quantities are closely related to counterparts found in general relativity. A lattice model with long-range spin-spin coupling is studied. This is compared with systems such as those encountered in general relativity and gravitating systems with Newtonian-type interactions. A long-range lattice model is presented which can be seen as a black hole analog. One finds that the analog's temperature and entropy have many properties which are found in black holes. Finally, the entropy scaling behavior of a gravitating perfect fluid of constant density is calculated. For weak interactions, the entropy scales like the volume of the system. As the interactions become stronger, the entropy becomes higher near the surface of the system, and becomes more area scaling. PMID:12935201
Ising-Glauber Spin Cluster Model for Temperature-Dependent Magnetization Noise in SQUIDs
NASA Astrophysics Data System (ADS)
De, Amrit
2014-11-01
Clusters of interacting two-level-systems, likely due to Farbe+(F+) centers at the metal-insulator interface, are shown to self-consistently lead to 1 /fα magnetization noise [with α (T )≲1 ] in SQUIDs. Model calculations, based on a new method of obtaining correlation functions, explains various puzzling experimental features. It is shown why the inductance noise is inherently temperature dependent while the flux noise is not, despite the same underlying microscopics. Magnetic ordering in these systems, established by three-point correlation functions, explains the observed flux- inductance-noise cross correlations. Since long-range ferromagnetic interactions are shown to lead to a more weakly temperature dependent flux noise when compared to short-range interactions, the time reversal symmetry of the clusters is also not likely broken by the same mechanism which mediates surface ferromagnetism in nanoparticles and thin films of the same insulator materials.
Ivanov, Dmitri A; Abanov, Alexander G
2013-02-01
We propose to describe correlations in classical and quantum systems in terms of full counting statistics of a suitably chosen discrete observable. The method is illustrated with two exactly solvable examples: the classical one-dimensional Ising model and the quantum spin-1/2 XY chain. For the one-dimensional Ising model, our method results in a phase diagram with two phases distinguishable by the long-distance behavior of the Jordan-Wigner strings. For the anisotropic spin-1/2 XY chain in a transverse magnetic field, we compute the full counting statistics of the magnetization and use it to classify quantum phases of the chain. The method, in this case, reproduces the previously known phase diagram. We also discuss the relation between our approach and the Lee-Yang theory of zeros of the partition function. PMID:23496467
Yang, Y. S.; Marsiglio, F.; Madsen, M.; Gaulin, Bruce D.; Rogge, R. B.; Fernandez-Baca, Jaime A
2002-01-01
Inelastic neutron-scattering profiles of spin waves in the dilute quasi-one-dimensional Ising-like antiferromagnet CsCo{sub 0.83}Mg{sub 0.17}Br{sub 3} have been investigated. Calculations of S{sup xx}(Q,{omega}), based on an effective spin Hamiltonian, accurately describe the experimental spin-wave spectrum of the 2J mode. The Q dependence of the energy of this spin-wave mode follows the analytical prediction {omega}{sub xx}(Q)=(2J)(1-5{var_epsilon}{sup 2}cos{sup 2}Qa+2{var_epsilon}{sup 2}){sup 1/2}, calculated by Ishimura and Shiba using perturbation theory.
Fritsch, Katharina; Ehlers, G.; Rule, K. C.; Habicht, Klaus; Ramazanoglu, Mehmet K.; Dabkowska, H. A.; Gaulin, Bruce D.
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_{3}V_{2}O_{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_{0}H_{c1}~6.25 T and μ_{0}H_{c2}~7 T is discontinuous, while the final quantum critical point at μ_{0}H_{c3}~13 T is continuous.
Creutz, M.
1985-01-01
The author discusses a reversible deterministic dynamics for Ising spins. The algorithm is a variation of microcanonical Monte Carlo techniques and is easily implemented with simple bit manipulation. This provides fast programs to study non-equilibrium phenomena such as heat flow.
Ising, Schelling and self-organising segregation
NASA Astrophysics Data System (ADS)
Stauffer, D.; Solomon, S.
2007-06-01
The similarities between phase separation in physics and residential segregation by preference in the Schelling model of 1971 are reviewed. Also, new computer simulations of asymmetric interactions different from the usual Ising model are presented, showing spontaneous magnetisation (=self-organising segregation) and in one case a sharp phase transition.
Spatially clustered zealots in a two-dimensional voter model
NASA Astrophysics Data System (ADS)
Stone, Thomas; Ludden, Matthew; McKay, Susan
The voter model, solvable in all dimensions in its standard form, has been extensively used to study behavior dynamics by using the tools of statistical mechanics. Recently, much work has been focused on determining the effects of zealots in the voter model, where a zealot is an agent that maintains its opinion (akin to an Ising spin variable) no matter the local environment. Here we investigate the effects of spatially clustered zealots in the standard voter model on a two-dimensional square lattice. The clustering of zealots is quantified by the conditional probability that a zealot of the +1 state appears on an adjacent site to a randomly chosen zealot. (All zealots are of the +1 state.) We determine the functional forms of the system consensus time with respect to system size, clustering, and zealot density, and compare these findings to previous results that do not include clustering. We also discuss an interesting random walk problem that arises when one attempts to calculate how clustering affects the consensus time for fixed zealot density and system size.
NASA Astrophysics Data System (ADS)
Jackson, Dennis L.
We developed a model to investigate the dielectric properties of the BaTiO3 - Bi(Zn 1/2Ti1/2)O3 (BT-BZT) solid solution, which is a relaxor ferroelectric and exhibits long range disorder. The model uses ab initio methods to determine all polarization states for every atomic configuration of 2x2x2 supercells of BT-BZT. Each supercell is placed on a lattice with an Ising-like interaction between neighboring cell polarizations. This method allows us to consider long range disorder, which is not possible with ab initio methods alone, and is required to properly understand relaxor ferroelectric materials. We analyze the Monte Carlo data for a single lattice configuration using the multiple histogram method, and develop a modified histogram technique to combine data from multiple lattice configurations. Our calculated values of dielectric constant, specific heat, and polarization agree reasonably well with experiment.
NASA Technical Reports Server (NTRS)
Knoll, R.; Epstein, G.; Hoang, S.; Huntzinger, G.; Steinberg, J. L.; Fainberg, J.; Grena, F.; Stone, R. G.; Mosier, S. R.
1978-01-01
The SBH experiment on ISEE-C will provide maps of the large scale structure of the interplanetary magnetic field from ten solar radii altitude to the earth orbit, in and out of the ecliptic. The SBH instrument will track type III solar radio bursts at 24 frequencies in the range 30 kHz-2 MHz thus providing the positions of 24 points along the line of force which guides the electrons producing the radio radiation. The antennas are two dipoles: one (90 m long) in the spin plane, the other (15 m long) along the spin axis. The receiver was designed for high sensitivity (0.3 microV in 3 kHz BW), high intermodulation rejection (80 dB/1 microV input for order 2 products), large dynamic range (70 dB), high selectivity (-30-dB response 6.5 kHz away from the center frequency of 10.7 MHz for the 3 kHz BW channels), and high reliability (expected orbital life: 3 years).
Complete analyticity for 2D Ising completed
NASA Astrophysics Data System (ADS)
Schonmann, Roberto H.; Shlosman, Senya B.
1995-06-01
We study the behavior of the two-dimensional nearest neighbor ferromagnetic Ising model under an external magnetic field h. We extend to every subcritical value of the temperature a result previously proven by Martirosyan at low enough temperature, and which roughly states that for finite systems with — boundary conditions under a positive external field, the boundary effect dominates in the bulk if the linear size of the system is of order B/h with B small enough, while if B is large enough, then the external field dominates in the bulk. As a consequence we are able to complete the proof that “complete analyticity for nice sets” holds for every value of the temperature and external field in the interior of the uniqueness region in the phase diagram of the model. The main tools used are the results and techniques developed to study large deviations for the block magnetization in the absence of the magnetic field, and recently extended to all temperatures below the critical one by Ioffe.
ISE System Development Methodology Manual
Hayhoe, G.F.
1992-02-17
The Information Systems Engineering (ISE) System Development Methodology Manual (SDM) is a framework of life cycle management guidelines that provide ISE personnel with direction, organization, consistency, and improved communication when developing and maintaining systems. These guide-lines were designed to allow ISE to build and deliver Total Quality products, and to meet the goals and requirements of the US Department of Energy (DOE), Westinghouse Savannah River Company, and Westinghouse Electric Corporation.
NASA Astrophysics Data System (ADS)
Renklioglu, B.; Yalabik, M. C.
2012-12-01
Phase transitions of the two-finite temperature Ising model on a square lattice are investigated by using a position space renormalization group (PSRG) transformation. Different finite temperatures, T x and T y , and also different time-scale constants, α x and α y for spin exchanges in the x and y directions define the dynamics of the non-equilibrium system. The critical surface of the system is determined by RG flows as a function of these exchange parameters. The Onsager critical point (when the two temperatures are equal) and the critical temperature for the limit when the other temperature is infinite, previously studied by the Monte Carlo method, are obtained. In addition, two steady-state fixed points which correspond to the non-equilibrium phase transition are presented. These fixed points yield the different universality class properties of the non-equilibrium phase transitions.
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.
Sparse High Dimensional Models in Economics
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
One-dimensional frustrated plaquette compass model: Nematic phase and spontaneous multimerization
NASA Astrophysics Data System (ADS)
Brzezicki, Wojciech; Oleś, Andrzej M.
2016-06-01
We introduce a one-dimensional (1D) pseudospin model on a ladder where the Ising interactions along the legs and along the rungs alternate between XiXi +1 and ZiZi +1 for even/odd bond (rung). We include also the next-nearest-neighbor Ising interactions on plaquettes' diagonals that alternate in such a way that a model where only leg interactions are switched on is equivalent to the one when only the diagonal ones are present. Thus in the absence of rung interactions the model can interpolate between two 1D compass models. The model possesses local symmetries which are the parities within each 2 ×2 cell (plaquette) of the ladder. We find that for different values of the interaction it can realize ground states that differ by the patterns formed by these local parities. By exact diagonalization we derive detailed phase diagrams for small systems of L =4 , 6, and 8 plaquettes, and use next L =12 to identify generic phases that appear in larger systems as well. Among them we find a nematic phase with macroscopic degeneracy when the leg and diagonal interactions are equal and the rung interactions are larger than a critical value. By performing a perturbative expansion around this phase we find indeed a very complex competition around the nematic phase which has to do with releasing frustration in this range of parameters. The nematic phase is similar to the one found in the two-dimensional compass model. For particular parameters the low-energy sector of the present plaquette model reduces to a 1D compass model with spins S =1 which suggests that it realizes peculiar crossovers within the class of compass models. Finally, we show that the model can realize phases with broken translation invariance which can be either dimerized, trimerized, etc., or completely disordered and highly entangled in a well identified window of the phase diagram.
NASA Astrophysics Data System (ADS)
Atitoaie, Alexandru; Stoleriu, Laurentiu; Tanasa, Radu; Stancu, Alexandru; Enachescu, Cristian
2016-04-01
The scientific community is manifesting a high research interest on spin crossover compounds and their recently synthesized nanoparticles, due to their various appealing properties, such as the bistability between a diamagnetic low spin state and a paramagnetic high spin state (HS), inter-switchable by temperature or pressure changes, light irradiation or magnetic field. The utility of these compounds showing hysteresis covers a broad area of applications, from the development of more efficient designs of temperature and pressure sensors to automotive and aeronautic industries and even a new type of molecular actuators. We are proposing in this work a study regarding the kinetic effects and the distribution of reversible and irreversible components on the thermal hysteresis of spin crossover nanoparticulated systems. We are considering here tridimensional systems with different sizes and also systems of nanoparticles with a Gaussian size distribution. The correlations between the kinetics of the thermal hysteresis, the distributions of sizes and intermolecular interactions and the transition temperature distributions were established by using the FORC (First Order Reversal Curves) method using a Monte Carlo technique within an Ising-like system.
Nonequilibrium behaviors of the three-dimensional Heisenberg model in the Swendsen-Wang algorithm
NASA Astrophysics Data System (ADS)
Nonomura, Yoshihiko; Tomita, Yusuke
2016-01-01
Recently, it was shown [Y. Nonomura, J. Phys. Soc. Jpn. 83, 113001 (2014), 10.7566/JPSJ.83.113001] that the nonequilibrium critical relaxation of the two-dimensional (2D) Ising model from a perfectly ordered state in the Wolff algorithm is described by stretched-exponential decay, and a universal scaling scheme was found to connect nonequilibrium and equilibrium behaviors. In the present study we extend these findings to vector spin models, and the 3D Heisenberg model could be a typical example. To evaluate the critical temperature and critical exponents precisely using the above scaling scheme, we calculate nonequilibrium ordering from the perfectly disordered state in the Swendsen-Wang algorithm, and we find that the critical ordering process is described by stretched-exponential growth with a comparable exponent to that of the 3D X Y model. The critical exponents evaluated in the present study are consistent with those in previous studies.
Thermal-Cycle Memory Functions and Ising Dynamics
NASA Astrophysics Data System (ADS)
Johnson, Brad; Patrick, David
2008-03-01
The Ising model provides a rich system for the study of a variety of correlated systems. In this talk, we present the results of numerical studies of 2- and 3-dimensional Ising spin systems subjected to thermal cycling from an ordered state to states with a fixed order parameter (<1), but with differing overall morphologies, and back to a quenched state. We find that for systems with initial states generated by thermal disordering above Tc, the initial state of a given order parameter has larger `islands' of like-spin (than the case for random disorder with the same overall order parameter) and consequent quenches of the state to T is the average quenched order parameter, and B is a constant that depends upon the morphology of the initial state. The reason for the strong correlation stems from the energies associated with spins at the borders of large clusters. This `memory effect' does not occur in 3D (due to the larger number of near-neighbors). Finally, we discuss the `memory function' in the context of interfacial states of liquid crystals.
Experimental realization of a compressed quantum simulation of a 32-spin Ising chain.
Li, Zhaokai; Zhou, Hui; Ju, Chenyong; Chen, Hongwei; Zheng, Wenqiang; Lu, Dawei; Rong, Xing; Duan, Changkui; Peng, Xinhua; Du, Jiangfeng
2014-06-01
Certain n-qubit quantum systems can be faithfully simulated by quantum circuits with only O(log(n)) qubits [B. Kraus, Phys. Rev. Lett. 107, 250503 (2011)]. Here we report an experimental realization of this compressed quantum simulation on a one-dimensional Ising chain. By utilizing an nuclear magnetic resonance quantum simulator with only five qubits, the property of ground-state magnetization of an open-boundary 32-spin Ising model is experimentally simulated, prefacing the expected quantum phase transition in the thermodynamic limit. This experimental protocol can be straightforwardly extended to systems with hundreds of spins by compressing them into up to merely 10-qubit systems. Our experiment paves the way for exploring physical phenomena in large-scale quantum systems with quantum simulators under current technology. PMID:24949746
Ising lines: Natural topological defects within ferroelectric Bloch walls
NASA Astrophysics Data System (ADS)
Stepkova, V.; Marton, P.; Hlinka, J.
2015-09-01
Phase-field simulations demonstrate that the polarization order-parameter field in the Ginzburg-Landau-Devonshire model of rhombohedral ferroelectric BaTiO3 allows for an interesting linear defect, stable under simple periodic boundary conditions. This linear defect, here called the Ising line, can be described as an about 2-nm-thick intrinsic paraelectric nanorod acting as a highly mobile borderline between finite portions of Bloch-like domain walls of opposite helicity. These Ising lines play the role of domain boundaries associated with the Ising-to-Bloch domain-wall phase transition.
NASA Astrophysics Data System (ADS)
Huang, Ran; Purushottam, D. Gujrati
2015-09-01
Two types of recursive lattices with the identical coordination number but different unit cells (2-D square and 3-D cube) are constructed and the antiferromagnetic Ising model is solved exactly on them to study the stable and metastable states. A multi-branched structure of the 2-D plaquette model, which we introduced in this work, makes it possible to be an analog to the cubic lattice. Two solutions of each model can be found to exhibit the crystallization of liquid, and the ideal glass transition of supercooled liquid respectively. Based on the solutions, the thermodynamics on both lattices, e.g. the free energy, energy density, and entropy of the supercooled liquid, crystal, and liquid state of the model are calculated and compared with each other. Interactions between particles farther away than the nearest neighbor distance and multi-spins interactions are taken into consideration, and their effects on the thermal behavior are examined. The two lattices show comparable properties on the thermodynamics, which proves that both of them are practical to describe the regular 3-D case, especially to locate the ideal glass transition, while the 2-D multi-branched plaquette model is less accurate with the advantage of simpler formulation and less computation time consumption. Supported by National Natural Science Foundation of China under Grant No. 11505110
Extra-dimensional models on the lattice
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
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. PMID:27415388
NASA Astrophysics Data System (ADS)
Fytas, Nikolaos G.; Martín-Mayor, Víctor
2016-06-01
It was recently shown [Phys. Rev. Lett. 110, 227201 (2013), 10.1103/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.
Robustness of topological quantum codes: Ising perturbation
NASA Astrophysics Data System (ADS)
Zarei, Mohammad Hossein
2015-02-01
We study the phase transition from two different topological phases to the ferromagnetic phase by focusing on points of the phase transition. To this end, we present a detailed mapping from such models to the Ising model in a transverse field. Such a mapping is derived by rewriting the initial Hamiltonian in a new basis so that the final model in such a basis has a well-known approximated phase transition point. Specifically, we consider the toric codes and the color codes on various lattices with Ising perturbation. Our results provide a useful table to compare the robustness of the topological codes and to explicitly show that the robustness of the topological codes depends on triangulation of their underlying lattices.
THREE-DIMENSIONAL MODEL FOR HYPERTHERMIA CALCULATIONS
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...
NASA Astrophysics Data System (ADS)
Yunus, ćaǧın; Renklioǧlu, 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.
Ferrimagnetic behaviors in a transverse Ising nanoisland
NASA Astrophysics Data System (ADS)
Kaneyoshi, T.
2016-05-01
In this paper, the phase diagrams and magnetizations of a magnetic nanoisland described by the transverse Ising model (TIM) are investigated by the use of the effective-field theory (EFT) with correlations. A lot of characteristic behaviors observed in standard ferrimagnetic materials as well as novel phenomena have been obtained, although the system consists of two finite spin-1/2 layers coupled antiferromagnetically with a negative interlayer coupling.
Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.
2006-06-01
From an experimental-mathematical perspective we analyze"Ising-class" integrals. Our experimental results involvedextreme-precision, multidimensional quadrature on intricate integrands;thus, highly parallel computation was required.
[Dimensional modeling analysis for outpatient payments].
Guo, Yi-zhong; Guo, Yi-min
2008-09-01
This paper introduces a data warehouse model for outpatient payments, which is designed according to the requirements of the hospital financial management while dimensional modeling technique is combined with the analysis on the requirements. This data warehouse model can not only improve the accuracy of financial management requirements, but also greatly increase the efficiency and quality of the hospital management. PMID:19119657
NASA Astrophysics Data System (ADS)
Cabrera, Ivelisse; Thompson, J. D.; Coldea, R.; Prabhakaran, D.; Bewley, R. I.; Guidi, T.; Rodriguez-Rivera, J. A.; Stock, C.
We report extensive single-crystal inelastic neutron scattering measurements of the magnetic excitations in the quasi 1D Ising ferromagnet CoNb2O6 in the quantum paramagnetic phase to characterize the effects of the finite interchain couplings. In this phase, we observe that excitations have a sharp, resolution-limited line shape at low energies and over most of the dispersion bandwidth, as expected for spin-flip quasiparticles. We map the full bandwidth along the strongly dispersive chain direction and resolve clear modulations of the dispersions in the plane normal to the chains, characteristic of frustrated interchain couplings in an antiferromagnetic isosceles triangular lattice. The dispersions can be well parametrized using a linear spin-wave model that includes interchain couplings and further neighbor exchanges. The observed dispersion bandwidth along the chain direction is smaller than that predicted by a linear spin-wave model using exchange values determined at zero field. We attribute this effect to quantum renormalization of the dispersion beyond the spin-wave approximation in fields slightly above the critical field, where quantum fluctuations are still significant. We acknowledge support from EPSRC Grant No. EP/H014934/1, the Oxford Clarendon Fund Scholarship and NSERC of Canada.
NASA Astrophysics Data System (ADS)
Prudnikov, Vladimir V.; Prudnikov, Pavel V.; Pospelov, Evgeny A.
2016-04-01
We have performed a numerical investigation of the influence of disorder on the dynamical non-equilibrium evolution of a 3D site-diluted Ising model from a low-temperature initial state with magnetization m 0 = 1. It is shown that two-time dependences of the autocorrelation and integrated response functions for systems with spin concentrations p = 1.0, 0.95, 0.8, 0.6 and 0.5 demonstrate ageing properties with anomalous slowing-down relaxation and violation of the fluctuation-dissipation ratio. It was revealed that during non-equilibrium critical dynamics in the long-time regime t-{{t}\\text{w}}\\gg {{t}\\text{w}}\\gg 1 the autocorrelation functions for diluted systems are extremely slow due to the pinning of domain walls on impurity sites. We have found that the fluctuation-dissipation ratio {{X}∞}=0 for diluted systems with spin concentration p < 1 while the pure system is characterized by {{X}∞}=0.784(7) . The autocorrelation function power-law delay becomes the same as for the time dependence of the magnetization in the critical point and is characterized by exponent -β /zν . Also, for diluted systems we reveal memory effects for critical evolution in the ageing regime with realization of cyclic temperature change and quenching at T<{{T}\\text{c}} .
3-Dimensional Topographic Models for the Classroom
NASA Technical Reports Server (NTRS)
Keller, J. W.; Roark, J. H.; Sakimoto, S. E. H.; Stockman, S.; Frey, H. V.
2003-01-01
We have recently undertaken a program to develop educational tools using 3-dimensional solid models of digital elevation data acquired by the Mars Orbital Laser Altimeter (MOLA) for Mars as well as a variety of sources for elevation data of the Earth. This work is made possible by the use of rapid prototyping technology to construct solid 3-Dimensional models of science data. We recently acquired rapid prototyping machine that builds 3-dimensional models in extruded plastic. While the machine was acquired to assist in the design and development of scientific instruments and hardware, it is also fully capable of producing models of spacecraft remote sensing data. We have demonstrated this by using Mars Orbiter Laser Altimeter (MOLA) topographic data and Earth based topographic data to produce extruded plastic topographic models which are visually appealing and instantly engage those who handle them.
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.
Complexity and Ability in Ising Games
NASA Astrophysics Data System (ADS)
Ramirez, Ayax; George, Michael
2008-03-01
In previous work [1, 2], we discussed various facets of designs in games, and considered the evolution [2] of Ising games. The traditional aspect of game theory, with its focus on rational decisions, was not considered in this work. Instead, there was a predominant interest in the time evolution of design toward a goal design, and resulting levels of frustration. There was also a concern with time- reversal properties. In the new work, our goal is to consider the molecular structureof the Ising model as it evolves, and to associate this molecular structure with feedback into the structure that can be understood in algorithmic terms. We develop an analogy with the famous Malthusian argument concerning exponential population increase, associating ability to cope with complexity, and algorithmic complexity, and discuss biological implications of the ideas associated with these games. [1] M. George, A nonequilibrium statistical model based on latin squares, paper presented at WorldComp'07, Las Vegas, Nevada, June 25-28, 2007. [2] M. George, Classical and quantum Ising games, paper presented at Fourth International Conference in Applied Mathematics and Computing, Plovdiv, Bulgaria, August, 2007.
Proper encoding for snapshot-entropy scaling in two-dimensional classical spin models
NASA Astrophysics Data System (ADS)
Matsueda, Hiroaki; Ozaki, Dai
2015-10-01
We reexamine the snapshot entropy of the Ising and three-states Potts models on the L ×L square lattice. Focusing on how to encode the spin snapshot, we find that the entropy at Tc scales asymptotically as S ˜(1 /3 )lnL that strongly reminds us of the entanglement entropy in one-dimensional quantum critical systems. This finding seems to support that the snapshot entropy after the proper encoding is related to the holographic entanglement entropy. On the other hand, the anomalous scaling Sχ˜χηlnχ for the coarse-grained snapshot entropy holds even for the proper encoding. These features originate in the fact that the largest singular value of the snapshot matrix is regulated by the proper encoding.
Improved fair sampling of ground states in Ising spin glasses
NASA Astrophysics Data System (ADS)
Katzgraber, Helmut G.; Zhu, Zheng; Ochoa, Andrew J.
2015-03-01
Verifying that an optimization approach can sample all solutions that minimize a Hamiltonian is a stringent test for any newly-developed algorithm. While most solvers easily compute the minimum of a cost function for small to moderate input sizes, equiprobable sampling of all ground-state configurations (within Poissonian fluctuations) is much harder to obtain. Most notably, methods such as transverse-field quantum annealing fail in passing this test for certain highly-degenerate problems. Here we present an attempt to sample ground states for Ising spin glasses based on a combination of low-temperature parallel tempering Monte Carlo combined with the cluster algorithm by Houdayer. Because the latter is rejection free and obeys details balance, the ground-state manifold is efficiently sampled. We illustrate the approach for Ising spin glasses on the D-Wave Two quantum annealer topology, known as the Chimera graph, as well as two-dimensional Ising spin glasses.
The Ising Decision Maker: a binary stochastic network for choice response time.
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. PMID:25090426
Finite-Temperature Spin Dynamics in a Perturbed Quantum Critical Ising Chain with an E8 Symmetry
NASA Astrophysics Data System (ADS)
Wu, Jianda; Kormos, Márton; Si, Qimiao
2014-12-01
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 .
Arai, Ryoichi; Fukui, Sadaharu; Kobayashi, Naoya; Sekiguchi, Junichi
2012-01-01
In Bacillus subtilis, LytE, LytF, CwlS, and CwlO are vegetative autolysins, dl-endopeptidases in the NlpC/P60 family, and play essential roles in cell growth and separation. IseA (YoeB) is a proteinaceous inhibitor against the dl-endopeptidases, peptidoglycan hydrolases. Overexpression of IseA caused significantly long chained cell morphology, because IseA inhibits the cell separation dl-endopeptidases post-translationally. Here, we report the first three-dimensional structure of IseA, determined by NMR spectroscopy. The structure includes a single domain consisting of three α-helices, one 310-helix, and eight β-strands, which is a novel fold like a “hacksaw.” Noteworthy is a dynamic loop between β4 and the 310-helix, which resembles a “blade.” The electrostatic potential distribution shows that most of the surface is positively charged, but the region around the loop is negatively charged. In contrast, the LytF active-site cleft is expected to be positively charged. NMR chemical shift perturbation of IseA interacting with LytF indicated that potential interaction sites are located around the loop. Furthermore, the IseA mutants D100K/D102K and G99P/G101P at the loop showed dramatic loss of inhibition activity against LytF, compared with wild-type IseA, indicating that the β4–310 loop plays an important role in inhibition. Moreover, we built a complex structure model of IseA-LytF by docking simulation, suggesting that the β4–310 loop of IseA gets stuck deep in the cleft of LytF, and the active site is occluded. These results suggest a novel inhibition mechanism of the hacksaw-like structure, which is different from known inhibitor proteins, through interactions around the characteristic loop regions with the active-site cleft of enzymes. PMID:23091053
Arai, Ryoichi; Fukui, Sadaharu; Kobayashi, Naoya; Sekiguchi, Junichi
2012-12-28
In Bacillus subtilis, LytE, LytF, CwlS, and CwlO are vegetative autolysins, DL-endopeptidases in the NlpC/P60 family, and play essential roles in cell growth and separation. IseA (YoeB) is a proteinaceous inhibitor against the DL-endopeptidases, peptidoglycan hydrolases. Overexpression of IseA caused significantly long chained cell morphology, because IseA inhibits the cell separation DL-endopeptidases post-translationally. Here, we report the first three-dimensional structure of IseA, determined by NMR spectroscopy. The structure includes a single domain consisting of three α-helices, one 3(10)-helix, and eight β-strands, which is a novel fold like a "hacksaw." Noteworthy is a dynamic loop between β4 and the 3(10)-helix, which resembles a "blade." The electrostatic potential distribution shows that most of the surface is positively charged, but the region around the loop is negatively charged. In contrast, the LytF active-site cleft is expected to be positively charged. NMR chemical shift perturbation of IseA interacting with LytF indicated that potential interaction sites are located around the loop. Furthermore, the IseA mutants D100K/D102K and G99P/G101P at the loop showed dramatic loss of inhibition activity against LytF, compared with wild-type IseA, indicating that the β4-3(10) loop plays an important role in inhibition. Moreover, we built a complex structure model of IseA-LytF by docking simulation, suggesting that the β4-3(10) loop of IseA gets stuck deep in the cleft of LytF, and the active site is occluded. These results suggest a novel inhibition mechanism of the hacksaw-like structure, which is different from known inhibitor proteins, through interactions around the characteristic loop regions with the active-site cleft of enzymes. PMID:23091053
Critical behavior of two-dimensional models with spatially modulated phases: Analytic results
NASA Astrophysics Data System (ADS)
Ruján, P.
1981-12-01
The two-dimensional Elliott [or axial next-nearest-neighbor Ising (ANNNI)] model is mapped into an eight-vertex model with direct and staggered fields. With the use of the transfer-matrix approach it is shown that the dual of the ANNNI model belongs to the universality class of the one-dimensional quantum XY model in a staggered field at T=0. The phase structure is investigated by high- and low-temperature expansions of the correlation length and by spin-wave-like approximations valid in first order at low and high temperatures, respectively. The fact that the phase diagram obtained at low temperatures agrees qualitatively with recent results by Villain and Bak and by Coppersmith et al. shows that the paramagnetic phase extends until T=0. The role of the umklapp scattering in determining the critical wave vector in the modulated phase and in stabilizing the <2> antiphase is pointed out. In the eight-vertex representation the critical indices are identified in the floating, massless phase. The dislocations destabilizing this incommensurate phase correspond to the energy operator of the eight-vertex model. Finally, it is argued that the apparent contradiction between the low-temperature results on one hand, and the Monte Carlo simulations and high-temperature-expansion results on the other hand, is probably due to the strong oscillatory behavior of spin-spin correlation functions in the massive paramagnetic region.
ISEE-1 and ISEE-2 fast plasma experiment and the ISEE-1 solar wind experiment
NASA Technical Reports Server (NTRS)
Bame, S. J.; Asbridge, J. R.; Felthauser, H. E.; Glore, J. P.; Paschmann, G.; Hemmerich, P.; Lehmann, K.; Rosenbauer, H.
1978-01-01
Identical fast plasma experiment (FPE) systems were placed on the ISEE-1 and ISEE-2 spacecraft. The FPE consists of three high efficiency 90 deg spherical section electrostatic analyzers using large secondary emitters and discrete dynode multipliers to detect analyzed particles. Two of them, viewing in opposite directions, produce complete 2D velocity distribution measurements of both protons and electrons every spacecraft revolution. A third FPE analyzer with a divided emitter measures 3D distributions at a slower rate. ISEE-1 also carries a solar-wind experiment (SWE) to measure solar-wind ions with high resolution. The SWE is composed of two 150 deg spherical section analyzers using the same set of plates. The two acceptance fans are tilted with respect to each other so that 3D characteristics of the ion distributions can be derived.
Anisotropic 2-dimensional Robin Hood model
NASA Astrophysics Data System (ADS)
Buldyrev, Sergey; Cwilich, Gabriel; Zypman, Fredy
2009-03-01
We have considered the Robin Hood model introduced by Zaitsev[1] to discuss flux creep and depinning of interfaces in a two dimensional system. Although the model has been studied extensively analytically in 1-d [2], its scaling laws have been verified numerically only in that case. Recent work suggest that its properties might be important to understand surface friction[3], where its 2-dimensional properties are important. We show that in the 2-dimensional case scaling laws can be found provided one considers carefully the anisotropy of the model, and different ways of introducing that anisotropy lead to different exponents and scaling laws, in analogy with directed percolation, with which this model is closely related[4]. We show that breaking the rotational symmetry between the x and y axes does not change the scaling properties of the model, but the introduction of a preferential direction of accretion (``robbing'' in the language of the model) leads to new scaling exponents. [1] S.I.Zaitsev, Physica A189, 411 (1992) [2] M. Pacuzki, S. Maslov and P.Bak, Phys Rev. E53, 414 (1996) [3] S. Buldyrev, J. Ferrante and F. Zypman Phys. Rev E64, 066110 (2006) [4] G. Odor, Rev. Mod. Phys. 76, 663 (2004) .
An Ising spin state explanation for financial asset allocation
NASA Astrophysics Data System (ADS)
Horvath, Philip A.; Roos, Kelly R.; Sinha, Amit
2016-03-01
We build on the developments in the application of statistical mechanics, notably the identity of the spin degree of freedom in the Ising model, to explain asset price dynamics in financial markets with a representative agent. Specifically, we consider the value of an individual spin to represent the proportional holdings in various assets. We use partial moment arguments to identify asymmetric reactions to information and develop an extension of a plunging and dumping model. This unique identification of the spin is a relaxation of the conventional discrete state limitation on an Ising spin to accommodate a new archetype in Ising model-finance applications wherein spin states may take on continuous values, and may evolve in time continuously, or discretely, depending on the values of the partial moments.
ISEE-3 Microwave Filter Requirements
NASA Technical Reports Server (NTRS)
Galvez, J. L.; Marlin, H.; Stanton, P.
1984-01-01
The 64 m subnet is committed to support the International Sun Earth Explorer (ISEE-3) spacecraft. The uplink and one of the downlink frequencies will be respectively, 2090 and 2217 MHz. As these two frequencies fall outside the normal DSN transmit and receive bands, the 64-m antennas present new filter requirements, which are analyzed.
NASA Astrophysics Data System (ADS)
Liu, Cheng-cheng; Shi, Jia-dong; Ding, Zhi-yong; Ye, Liu
2016-05-01
Quantum coherence is an important physical resource in quantum computation and quantum information processing. In this paper, we firstly obtain an uncertainty-like expression relating two coherences contained in corresponding local bipartite quantum system. This uncertainty-like inequality shows that the larger the coherence of one subsystem, the less coherence contained in other subsystems. Further, we discuss in detail the uncertainty-like relation among three single-partite quantum systems. We show that the coherence contained in pure tripartite quantum system is greater than the sum of the coherence of all local subsystems.
Quantum entanglement in the one-dimensional spin-orbital SU (2 )⊗XXZ model
NASA Astrophysics Data System (ADS)
You, Wen-Long; Horsch, Peter; Oleś, Andrzej M.
2015-08-01
We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional SU (2 )⊗XXZ model with SU(2) spin exchange and anisotropic XXZ orbital exchange interactions and negative exchange coupling constant. As a unique feature, the spin-orbital entanglement entropy in the entangled ground states increases here linearly with system size. In the case of Ising orbital interactions, we identify an emergent phase with long-range spin-singlet dimer correlations triggered by a quadrupling of correlations in the orbital sector. The peculiar translational-invariant spin-singlet dimer phase has finite von Neumann entanglement entropy and survives when orbital quantum fluctuations are included. It even persists in the isotropic SU (2 )⊗SU (2) limit. Surprisingly, for finite transverse orbital coupling, the long-range spin-singlet correlations also coexist in the antiferromagnetic spin and alternating orbital phase making this phase also unconventional. Moreover, we also find a complementary orbital singlet phase that exists in the isotropic case but does not extend to the Ising limit. The nature of entanglement appears essentially different from that found in the frequently discussed model with positive coupling. Furthermore, we investigate the collective spin and orbital wave excitations of the disentangled ferromagnetic-spin/ferro-orbital ground state and explore the continuum of spin-orbital excitations. Interestingly, one finds among the latter excitations two modes of exciton bound states. Their spin-orbital correlations differ from the remaining continuum states and exhibit logarithmic scaling of the von Neumann entropy with increasing system size. We demonstrate that spin-orbital excitons can be experimentally explored using resonant inelastic x-ray scattering, where the strongly entangled exciton states can be easily distinguished from the spin-orbital continuum.
Diluted Ising Magnet on the Bethe Lattice
NASA Astrophysics Data System (ADS)
Semkin, S. V.; Smagin, V. P.
2016-04-01
A solution is obtained for the Ising model on the Bethe lattice comprising a mixture of magnetic and nonmagnetic atoms in a thermodynamic equilibrium. The concentration and temperature dependences of spontaneous magnetization, the Curie temperature, and the percolation threshold are found together with the pair correlation functions of three types that characterize the arrangement of impurity atoms and the correlation of magnetic moments. It is demonstrated that the system with mobile impurities in the thermodynamic equilibrium can be brought closer to the system with frozen impurities by adjusting the parameters of interatomic interaction.
Ordering and phase transitions in random-field Ising systems
NASA Technical Reports Server (NTRS)
Maritan, Amos; Swift, Michael R.; Cieplak, Marek; Chan, Moses H. W.; Cole, Milton W.; Banavar, Jayanth R.
1991-01-01
An exact analysis of the Ising model with infinite-range interactions in a random field and a local mean-field theory in three dimensions is carried out leading to a phase diagram with several coexistence surfaces and lines of critical points. The results show that the phase diagram depends crucially on whether the distribution of random fields is symmetric or not. Thus, Ising-like phase transitions in a porous medium (the asymmetric case) are in a different universality class from the conventional random-field model (symmetric case).
Efficient cluster Monte Carlo algorithm for Ising spin glasses in more than two space dimensions
NASA Astrophysics Data System (ADS)
Ochoa, Andrew J.; Zhu, Zheng; Katzgraber, Helmut G.
2015-03-01
A cluster algorithm that speeds up slow dynamics in simulations of nonplanar Ising spin glasses away from criticality is urgently needed. In theory, the cluster algorithm proposed by Houdayer poses no advantage over local moves in systems with a percolation threshold below 50%, such as cubic lattices. However, we show that the frustration present in Ising spin glasses prevents the growth of system-spanning clusters at temperatures roughly below the characteristic energy scale J of the problem. Adding Houdayer cluster moves to simulations of Ising spin glasses for T ~ J produces a speedup that grows with the system size over conventional local moves. We show results for the nonplanar quasi-two-dimensional Chimera graph of the D-Wave Two quantum annealer, as well as conventional three-dimensional Ising spin glasses, where in both cases the addition of cluster moves speeds up thermalization visibly in the physically-interesting low temperature regime.
Two dimensional thick center vortex model
NASA Astrophysics Data System (ADS)
Rafibakhsh, Shahnoosh; Ahmadi, Alireza
2016-01-01
The potential between static color source is calculated in the SU (3) gauge group by introducing a two dimensional vortex flux. To generalize the model, the length of the Wilson loop is equal to R oriented along the x axis, and the vortex flux is considered as a function of x and y. The comparison between the generalized model and the original one shows that the intermediate linear regime is increased significantly and better agreement with Casimir scaling is achieved. Furthermore, the model is applied to calculate the potential between baryons.
Three-dimensional modeling of ovarian cancer
Erin, White; Hilary, Kenny; Ernst, Lengyel
2015-01-01
New models for epithelial ovarian cancer initiation and metastasis are required to obtain a mechanistic understanding of the disease and to develop new therapeutics. Modeling ovarian cancer however is challenging as a result of the genetic heterogeneity of the malignancy, the diverse pathology, the limited availability of human tissue for research, the atypical mechanisms of metastasis, and because the origin is unclear. Insights into the origin of high-grade serous ovarian carcinomas and mechanisms of metastasis have resulted in the generation of novel three-dimensional (3D) culture models that better approximate the behavior of the tumor cells in vivo than prior two-dimensional models. The 3D models aim to recapitulate the tumor microenvironment, which has a critical role in the pathogenesis of ovarian cancer. Ultimately, findings using models that accurately reflect human ovarian cancer biology are likely to translate into improved clinical outcomes. In this review we discuss the design of new 3D culture models of ovarian cancer primarily using human cells, key studies in which these models have been applied, current limitations, and future applications. PMID:25034878
Ising antiferromagnet on the Archimedean lattices.
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. PMID:26172675
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.
Finite-dimensional models of diffusion chaos
NASA Astrophysics Data System (ADS)
Glyzin, S. D.; Kolesov, A. Yu.; Rozov, N. Kh.
2010-05-01
Some parabolic systems of the reaction-diffusion type exhibit the phenomenon of diffusion chaos. Specifically, when the diffusivities decrease proportionally, while the other parameters of a system remain fixed, the system exhibits a chaotic attractor whose dimension increases indefinitely. Various finite-dimensional models of diffusion chaos are considered that represent chains of coupled ordinary differential equations and similar chains of discrete mappings. A numerical analysis suggests that these chains with suitably chosen parameters exhibit chaotic attractors of arbitrarily high dimensions.
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.
Nature versus nurture: predictability in low-temperature Ising dynamics.
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(-θ)(h) with θ(h)=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. PMID:24229093
Wave turbulence in one-dimensional models
NASA Astrophysics Data System (ADS)
Zakharov, V. E.; Guyenne, P.; Pushkarev, A. N.; Dias, F.
2001-05-01
A two-parameter nonlinear dispersive wave equation proposed by Majda, McLaughlin and Tabak is studied analytically and numerically as a model for the study of wave turbulence in one-dimensional systems. Our ultimate goal is to test the validity of weak turbulence theory. Although weak turbulence theory is independent on the sign of the nonlinearity of the model, the numerical results show a strong dependence on the sign of the nonlinearity. A possible explanation for this discrepancy is the strong influence of coherent structures - wave collapses and quasisolitons - in wave turbulence.
Structural Modelling of Two Dimensional Amorphous Materials
NASA Astrophysics Data System (ADS)
Kumar, Avishek
The continuous random network (CRN) model of network glasses is widely accepted as a model for materials such as vitreous silica and amorphous silicon. Although it has been more than eighty years since the proposal of the CRN, there has not been conclusive experimental evidence of the structure of glasses and amorphous materials. This has now changed with the advent of two-dimensional amorphous materials. Now, not only the distribution of rings but the actual atomic ring structure can be imaged in real space, allowing for greater charicterization of these types of networks. This dissertation reports the first work done on the modelling of amorphous graphene and vitreous silica bilayers. Models of amorphous graphene have been created using a Monte Carlo bond-switching method and MD method. Vitreous silica bilayers have been constructed using models of amorphous graphene and the ring statistics of silica bilayers has been studied.
Modelling of Three-Dimensional Nanographene.
Mathioudakis, Christos; Kelires, Pantelis C
2016-12-01
Monte Carlo simulations and tight-binding calculations shed light on the properties of three-dimensional nanographene, a material composed of interlinked, covalently-bonded nanoplatelet graphene units. By constructing realistic model networks of nanographene, we study its structure, mechanical stability, and optoelectronic properties. We find that the material is nanoporous with high specific surface area, in agreement with experimental reports. Its structure is characterized by randomly oriented and curved nanoplatelet units which retain a high degree of graphene order. The material exhibits good mechanical stability with a formation energy of only ∼0.3 eV/atom compared to two-dimensional graphene. It has high electrical conductivity and optical absorption, with values approaching those of graphene. PMID:26983431
Arbitrary dimensional Majorana dualities and architectures for topological matter
NASA Astrophysics Data System (ADS)
Nussinov, Zohar; Ortiz, Gerardo; Cobanera, Emilio
2012-08-01
Motivated by the prospect of attaining Majorana modes at the ends of nanowires, we analyze interacting Majorana systems on general networks and lattices in an arbitrary number of dimensions, and derive universal spin duals. We prove that these interacting Majorana systems, quantum Ising gauge theories, and transverse-field Ising models with annealed bimodal disorder are all dual to one another on general planar graphs. This leads to an interesting connection between heavily disordered annealed Ising systems and uniform Ising theories with nearest-neighbor interactions. As any Dirac fermion (including electronic) operator can be expressed as a linear combination of two Majorana fermion operators, our results further lead to dualities between interacting Dirac fermionic systems on rather general lattices and graphs and corresponding spin systems. Such general complex Majorana architectures (other than those of simple square or other crystalline arrangements) might be of empirical relevance. As these systems display low-dimensional symmetries, they are candidates for realizing topological quantum order. The spin duals allow us to predict the feasibility of various standard transitions as well as spin-glass-type behavior in interacting Majorana fermion or electronic systems. Several systems that can be simulated by arrays of Majorana wires are further introduced and investigated: (1) the XXZ honeycomb compass model (intermediate between the classical Ising model on the honeycomb lattice and Kitaev's honeycomb model), (2) a checkerboard lattice realization of the model of Xu and Moore for superconducting (p+ip) arrays, and a (3) compass-type two-flavor Hubbard model with both pairing and hopping terms. By the use of our dualities (tantamount to high-dimensional fermionization), we show that all of these systems lie in the three-dimensional Ising universality class. We further discuss how the existence of topological orders and bounds on autocorrelation times can be
An Artificial Ising System with Phononic Excitations
NASA Astrophysics Data System (ADS)
Ghaffari, Hamed; Griffith, W. Ashley; Benson, Philip; Nasseri, M. H. B.; Young, R. Paul
Many intractable systems and problems can be reduced to a system of interacting spins. Here, we report mapping collective phononic excitations from different sources of crystal vibrations to spin systems. The phononic excitations in our experiments are due to micro and nano cracking (yielding crackling noises due to lattice distortion). We develop real time mapping of the multi-array senores to a network-space and then mapping the excitation- networks to spin-like systems. We show that new mapped system satisfies the quench (impulsive) characteristics of the Ising model in 2D classical spin systems. In particular, we show that our artificial Ising system transits between two ground states and approaching the critical point accompanies with a very short time frozen regime, inducing formation of domains separated by kinks. For a cubic-test under a true triaxial test (3D case), we map the system to a 6-spin ring under a transversal-driving field where using functional multiplex networks, the vector components of the spin are inferred (i.e., XY model). By visualization of spin patterns of the ring per each event, we demonstrate that ``kinks'' (as defects) proliferate when system approach from above to its critical point. We support our observations with employing recorded acoustic excitations during distortion of crystal lattices in nano-indentation tests on different crystals (silicon and graphite), triaxial loading test on rock (poly-crystal) samples and a true 3D triaxial test.
Three-dimensional pancreas organogenesis models.
Grapin-Botton, A
2016-09-01
A rediscovery of three-dimensional culture has led to the development of organ biogenesis, homeostasis and disease models applicable to human tissues. The so-called organoids that have recently flourished serve as valuable models bridging between cell lines or primary cells grown on the bottom of culture plates and experiments performed in vivo. Though not recapitulating all aspects of organ physiology, the miniature organs generated in a dish are useful models emerging for the pancreas, starting from embryonic progenitors, adult cells, tumour cells and stem cells. This review focusses on the currently available systems and their relevance to the study of the pancreas, of β-cells and of several pancreatic diseases including diabetes. We discuss the expected future developments for studying human pancreas development and function, for developing diabetes models and for producing therapeutic cells. PMID:27615129
A fast vectorized program for the CDC cyber 205 to simulate the ising spin glass in three dimensions
NASA Astrophysics Data System (ADS)
Bhanot, Gyan; Salvador, Román; Duke, Dennis; Moriarty, K. J. M.
1988-06-01
We describe a computer program that performs the Metropolis algorithm for the three-dimensional ( J = ±1) Ising spin glass problem at a peak speed of 80 million spin updates per second on a 2-pipe CDC CYBER 205.
Violation of Lee-Yang circle theorem for Ising phase transitions on complex networks
NASA Astrophysics Data System (ADS)
Krasnytska, M.; Berche, B.; Holovatch, Yu.; Kenna, R.
2015-09-01
The Ising model on annealed complex networks with degree distribution decaying algebraically as p(K)∼ K-λ has a second-order phase transition at finite temperature if λ>3 . In the absence of space dimensionality, λ controls the transition strength; classical mean-field exponents apply for λ >5 but critical exponents are λ-dependent if λ < 5 . Here we show that, as for regular lattices, the celebrated Lee-Yang circle theorem is obeyed for the former case. However, unlike on regular lattices where it is independent of dimensionality, the circle theorem fails on complex networks when λ < 5 . We discuss the importance of this result for both theory and experiments on phase transitions and critical phenomena. We also investigate the finite-size scaling of Lee-Yang zeros in both regimes as well as the multiplicative logarithmic corrections which occur at λ=5 .
A three-dimensional asymmetric magnetopause model
NASA Astrophysics Data System (ADS)
Lin, R. L.; Zhang, X. X.; Liu, S. Q.; Wang, Y. L.; Gong, J. C.
2010-04-01
A new three-dimensional asymmetric magnetopause model has been developed for corrected GSM coordinates and parameterized by the solar wind dynamic and magnetic pressures (Pd + Pm), the interplanetary magnetic field (IMF) Bz, and the dipole tilt angle. On the basis of the magnetopause crossings from Geotail, IMP 8, Interball, TC1, Time History of Events and Macroscale Interactions during Substorms (THEMIS), Wind, Cluster, Polar, Los Alamos National Laboratory (LANL), GOES, and Hawkeye, and the corresponding upstream solar wind parameters from ACE, Wind, or OMNI, this model is constructed by the Levenberg-Marquardt method for nonlinear multiparameter fitting step-by-step over the divided regions. The asymmetries of the magnetopause and the indentations near the cusps are appropriately described in this new model. In addition, the saturation effect of IMF Bz on the subsolar distance and the extrapolation for the distant tail magnetopause are also considered. On the basis of this model, the power law index for the subsolar distance versus Pd + Pm is a bit less than -1/6, the northward IMF Bz almost does not influence the magnetopause, and the dipole tilt angle is very important to the north-south asymmetry and the location of indentations. In comparison with the previous empirical magnetopause models based on our database, the new model improves prediction capability to describe the three-dimensional structure of the magnetopause. It is shown that this new model can be used to quantitatively study how Pd + Pm compresses the magnetopause, how the southward IMF Bz erodes the magnetopause, and how the dipole tilt angle influences the north-south asymmetry and the indentations.
NASA Technical Reports Server (NTRS)
Denkins, Pamela S.; Saganti, P.; Obot, V.; Singleterry, R.
2006-01-01
This viewgraph document reviews the Radiation Interuniversity Science and Engineering (RaISE) Project, which is a project that has as its goals strengthening and furthering the curriculum in radiation sciences at two Historically Black Colleges and Universities (HBCU), Prairie View A&M University and Texas Southern University. Those were chosen in part because of the proximity to NASA Johnson Space Center, a lead center for the Space Radiation Health Program. The presentation reviews the courses that have been developed, both in-class, and on-line.
Schiek, Richard
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.
Low dimensional modeling of wall turbulence
NASA Astrophysics Data System (ADS)
Aubry, Nadine
2015-11-01
In this talk we will review the original low dimensional dynamical model of the wall region of a turbulent boundary layer [Aubry, Holmes, Lumley and Stone, Journal of Fluid Dynamics 192, 1988] and discuss its impact on the field of fluid dynamics. We will also invite a few researchers who would like to make brief comments on the influence Lumley had on their research paths. In collaboration with Philip Holmes, Program in Applied and Computational Mathematics and Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ.
Universal asymptotic statistics of maximal relative height in one-dimensional solid-on-solid models
NASA Astrophysics Data System (ADS)
Schehr, Grégory; Majumdar, Satya N.
2006-05-01
We study the probability density function P(hm,L) of the maximum relative height hm in a wide class of one-dimensional solid-on-solid models of finite size L . For all these lattice models, in the large- L limit, a central limit argument shows that, for periodic boundary conditions, P(hm,L) takes a universal scaling form P(hm,L)˜(12wL)-1f(hm/(12wL)) , with wL the width of the fluctuating interface and f(x) the Airy distribution function. For one instance of these models, corresponding to the extremely anisotropic Ising model in two dimensions, this result is obtained by an exact computation using the transfer matrix technique, valid for any L>0 . These arguments and exact analytical calculations are supported by numerical simulations, which show in addition that the subleading scaling function is also universal, up to a nonuniversal amplitude, and simply given by the derivative of the Airy distribution function f'(x) .
Taxonomy of particles in Ising spin chains.
Liu, Dan; Lu, Ping; Müller, Gerhard; Karbach, Michael
2011-08-01
The statistical mechanics of particles with shapes on a one-dimensional lattice is investigated in the context of the s=1 Ising chain with uniform nearest-neighbor coupling, quadratic single-site potential, and a magnetic field, which supports four distinct ground states: |↑↓↑↓⋯>, |∘∘⋯>, |↑↑⋯>, |↑∘↑∘⋯>. The complete spectrum is generated from each ground state by particles from a different set of six or seven species. Particles and elements of the pseudovacuum are characterized by motifs (patterns of several consecutive site variables). Particles are floating objects that can be placed into open slots on the lattice. Open slots are recognized as permissible links between motifs. The energy of a particle varies between species but is independent of where it is placed. Placement of one particle changes the open-slot configuration for particles of all species. This statistical interaction is encoded in a generalized Pauli principle, from which the multiplicity of states for a given particle combination is determined and used for the exact statistical mechanical analysis. Particles from all species belong to one of four categories: compacts, hosts, tags, or hybrids. Compacts and hosts find open slots in segments of pseudovacuum. Tags find open slots inside hosts. Hybrids are tags with hosting capability. In the taxonomy of particles proposed here, "species" is indicative of structure and "category" indicative of function. The hosting function splits the Pauli principle into exclusion and accommodation parts. Near phase boundaries, the state of the Ising chain at low temperature is akin to that of miscible or immiscible liquids with particles from one species acting as surfactant molecules. PMID:21928978
Three-dimensional ring current decay model
NASA Astrophysics Data System (ADS)
Fok, Mei Ching; Moore, Thomas E.; Kozyra, Janet U.; Ho, George C.; Hamilton, Douglas C.
1995-06-01
This work is an extension of a previous ring current decay model. In the previous work, a two-dimensional kinetic model was constructed to study the temporal variations of the equatorially mirroring ring current ions, considering charge exchange and Coulomb drag losses along drift paths in a magnetic dipole field. In this work, particles with arbitrary pitch angle are considered. By bounce averaging the kinetic equation of the phase space density, information along magnetic field lines can be inferred from the equator. The three-dimensional model is used to simulate the recovery phase of a model great magnetic storm, similar to that which occurred in early February 1986. The initial distribution of ring current ions (at the minimum Dst) is extrapolated to all local times from AMPTE/CCE spacecraft observations on the dawnside and duskside of the inner magnetosphere spanning the L value range L=2.25 to 6.75. Observations by AMPTE/CCE of ring current distributions over subsequent orbits during the storm recovery phase are compared to model outputs. In general, the calculated ion fluxes are consistent with observations, except for H+ fluxes at tens of keV, which are always overestimated. A newly invented visualization idea, designated as a chromogram, is used to display the spatial and energy dependence of the ring current ion diifferential flux. Important features of storm time ring current, such as day-night asymmetry during injection and drift hole on the dayside at low energies (<10 keV), are manifested in the chromogram representation. The pitch angle distribution is well fit by the function, j0(1+Ayn), where y is sine of the equatorial pitch angle. The evolution of the index n is a combined effect of charge exchange loss and particle drift. At low energies (<30 keV), both drift dispersion and charge exchange are important in determining n. ©American Geophysical 1995
Three-dimensional ring current decay model
NASA Technical Reports Server (NTRS)
Fok, Mei-Ching; Moore, Thomas E.; Kozyra, Janet U.; Ho, George C.; Hamilton, Douglas C.
1995-01-01
This work is an extension of a previous ring current decay model. In the previous work, a two-dimensional kinetic model was constructed to study the temporal variations of the equatorially mirroring ring current ions, considering charge exchange and Coulomb drag losses along drift paths in a magnetic dipole field. In this work, particles with arbitrary pitch angle are considered. By bounce averaging the kinetic equation of the phase space density, information along magnetic field lines can be inferred from the equator. The three-dimensional model is used to simulate the recovery phase of a model great magnetic storm, similar to that which occurred in early February 1986. The initial distribution of ring current ions (at the minimum Dst) is extrapolated to all local times from AMPTE/CCE spacecraft observations on the dawnside and duskside of the inner magnetosphere spanning the L value range L = 2.25 to 6.75. Observations by AMPTE/CCE of ring current distributions over subsequent orbits during the storm recovery phase are compared to model outputs. In general, the calculated ion fluxes are consistent with observations, except for H(+) fluxes at tens of keV, which are always overestimated. A newly invented visualization idea, designated as a chromogram, is used to display the spatial and energy dependence of the ring current ion differential flux. Important features of storm time ring current, such as day-night asymmetry during injection and drift hole on the dayside at low energies (less than 10 keV), are manifested in the chromogram representation. The pitch angle distribution is well fit by the function, J(sub o)(1 + Ay(sup n)), where y is sine of the equatorial pitch angle. The evolution of the index n is a combined effect of charge exchange loss and particle drift. At low energies (less than 30 keV), both drift dispersion and charge exchange are important in determining n.
Vlasov multi-dimensional model dispersion relation
Lushnikov, Pavel M.; Rose, Harvey A.; Silantyev, Denis A.; Vladimirova, Natalia
2014-07-15
A hybrid model of the Vlasov equation in multiple spatial dimension D > 1 [H. A. Rose and W. Daughton, Phys. Plasmas 18, 122109 (2011)], the Vlasov multi dimensional model (VMD), consists of standard Vlasov dynamics along a preferred direction, the z direction, and N flows. At each z, these flows are in the plane perpendicular to the z axis. They satisfy Eulerian-type hydrodynamics with coupling by self-consistent electric and magnetic fields. Every solution of the VMD is an exact solution of the original Vlasov equation. We show approximate convergence of the VMD Langmuir wave dispersion relation in thermal plasma to that of Vlasov-Landau as N increases. Departure from strict rotational invariance about the z axis for small perpendicular wavenumber Langmuir fluctuations in 3D goes to zero like θ{sup N}, where θ is the polar angle and flows are arranged uniformly over the azimuthal angle.
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
High dimensional decision dilemmas in climate models
NASA Astrophysics Data System (ADS)
Bracco, A.; Neelin, J. D.; Luo, H.; McWilliams, J. C.; Meyerson, J. E.
2013-05-01
An important source of uncertainty in climate models is linked to the calibration of model parameters. Interest in systematic and automated parameter optimization procedures stems from the desire to improve the model climatology and to quantify the average sensitivity associated with potential changes in the climate system. Neelin et al. (2010) used a quadratic metamodel to objectively calibrate an atmospheric circulation model (AGCM) around four adjustable parameters. The metamodel accurately estimates global spatial averages of common fields of climatic interest, from precipitation, to low and high level winds, from temperature at various levels to sea level pressure and geopotential height, while providing a computationally cheap strategy to explore the influence of parameter settings. Here, guided by the metamodel, the ambiguities or dilemmas related to the decision making process in relation to model sensitivity and optimization are examined. Simulations of current climate are subject to considerable regional-scale biases. Those biases may vary substantially depending on the climate variable considered, and/or on the performance metric adopted. Common dilemmas are associated with model revisions yielding improvement in one field or regional pattern or season, but degradation in another, or improvement in the model climatology but degradation in the interannual variability representation. Challenges are posed to the modeler by the high dimensionality of the model output fields and by the large number of adjustable parameters. The use of the metamodel in the optimization strategy helps visualize trade-offs at a regional level, e.g. how mismatches between sensitivity and error spatial fields yield regional errors under minimization of global objective functions.
High dimensional decision dilemmas in climate models
NASA Astrophysics Data System (ADS)
Bracco, A.; Neelin, J. D.; Luo, H.; McWilliams, J. C.; Meyerson, J. E.
2013-10-01
An important source of uncertainty in climate models is linked to the calibration of model parameters. Interest in systematic and automated parameter optimization procedures stems from the desire to improve the model climatology and to quantify the average sensitivity associated with potential changes in the climate system. Building upon on the smoothness of the response of an atmospheric circulation model (AGCM) to changes of four adjustable parameters, Neelin et al. (2010) used a quadratic metamodel to objectively calibrate the AGCM. The metamodel accurately estimates global spatial averages of common fields of climatic interest, from precipitation, to low and high level winds, from temperature at various levels to sea level pressure and geopotential height, while providing a computationally cheap strategy to explore the influence of parameter settings. Here, guided by the metamodel, the ambiguities or dilemmas related to the decision making process in relation to model sensitivity and optimization are examined. Simulations of current climate are subject to considerable regional-scale biases. Those biases may vary substantially depending on the climate variable considered, and/or on the performance metric adopted. Common dilemmas are associated with model revisions yielding improvement in one field or regional pattern or season, but degradation in another, or improvement in the model climatology but degradation in the interannual variability representation. Challenges are posed to the modeler by the high dimensionality of the model output fields and by the large number of adjustable parameters. The use of the metamodel in the optimization strategy helps visualize trade-offs at a regional level, e.g., how mismatches between sensitivity and error spatial fields yield regional errors under minimization of global objective functions.
Incorporating 3-dimensional models in online articles
Cevidanes, Lucia H. S.; Ruellasa, Antonio C. O.; Jomier, Julien; Nguyen, Tung; Pieper, Steve; Budin, Francois; Styner, Martin; Paniagua, Beatriz
2015-01-01
Introduction The aims of this article were to introduce the capability to view and interact with 3-dimensional (3D) surface models in online publications, and to describe how to prepare surface models for such online 3D visualizations. Methods Three-dimensional image analysis methods include image acquisition, construction of surface models, registration in a common coordinate system, visualization of overlays, and quantification of changes. Cone-beam computed tomography scans were acquired as volumetric images that can be visualized as 3D projected images or used to construct polygonal meshes or surfaces of specific anatomic structures of interest. The anatomic structures of interest in the scans can be labeled with color (3D volumetric label maps), and then the scans are registered in a common coordinate system using a target region as the reference. The registered 3D volumetric label maps can be saved in .obj, .ply, .stl, or .vtk file formats and used for overlays, quantification of differences in each of the 3 planes of space, or color-coded graphic displays of 3D surface distances. Results All registered 3D surface models in this study were saved in .vtk file format and loaded in the Elsevier 3D viewer. In this study, we describe possible ways to visualize the surface models constructed from cone-beam computed tomography images using 2D and 3D figures. The 3D surface models are available in the article’s online version for viewing and downloading using the reader’s software of choice. These 3D graphic displays are represented in the print version as 2D snapshots. Overlays and color-coded distance maps can be displayed using the reader’s software of choice, allowing graphic assessment of the location and direction of changes or morphologic differences relative to the structure of reference. The interpretation of 3D overlays and quantitative color-coded maps requires basic knowledge of 3D image analysis. Conclusions When submitting manuscripts, authors can
A three-dimensional human walking model
NASA Astrophysics Data System (ADS)
Yang, Q. S.; Qin, J. W.; Law, S. S.
2015-11-01
A three-dimensional human bipedal walking model with compliant legs is presented in this paper. The legs are modeled with time-variant dampers, and the model is able to characterize the gait pattern of an individual using a minimal set of parameters. Feedback control, for both the forward and lateral movements, is implemented to regulate the walking performance of the pedestrian. The model provides an improvement over classic invert pendulum models. Numerical studies were undertaken to investigate the effects of leg stiffness and attack angle. Simulation results show that when walking at a given speed, increasing the leg stiffness with a constant attack angle results in a longer step length, a higher step frequency, a faster walking speed and an increase in both the peak vertical and lateral ground reaction forces. Increasing the attack angle with a constant leg stiffness results in a higher step frequency, a decrease in the step length, an increase in the total energy of the system and a decrease in both the peak vertical and lateral ground reaction forces.
Three-dimensional model of lignin structure
Jurasek, L.
1995-12-01
An attempt to build a three-dimensional model of lignin structure using a computer program is described. The program simulates the biosynthesis of spruce lignin by allowing coniferyl alcohol subunits to be added randomly by six different types of linkages, assumed to be most common. The simulated biosynthesis starts from a number of seed points within restricted space, corresponding to 50 mM initial concentration of coniferyl alcohol. Rules of three-dimensional packing of the subunits within the lignin macro-molecule are observed during the simulated biosynthetic process. Branched oligomeric structures thus generated form crosslinks at those positions where the chains grow close enough to form a link. Inter-chain crosslinking usually joins the oligomers into one macromolecule. Intra-chain crosslinks are also formed and result in closed loops. Typically, a macromolecule with molecular weight of approx. 2 x 105 is formed, with internal density of 1.35g/cm3. Various characteristics of the internal structure, such as branching, crosslinking, bond frequencies, and chain length distribution are described. Breakdown of the polymer was also simulated and the effect of closed loops on the weight average molecular weight is shown. The effect of the shape of the biosynthetic space on the degree of crosslinking is discussed and predictions of the overall molecular shape of lignin particles are made.
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.…
Volumetric techniques: three-dimensional midface modeling
Pierzchała, Ewa; Placek, Waldemar
2014-01-01
Aging is a complex process caused by many factors. The most important factors include exposure to UV radiation, smoking, facial muscle movement, gravity, loss and displacement of fat and bone resorption. As a symptom of aging, face loses elasticity, volume and cheerful look. While changing face proportions, the dominant part of a face is its bottom instead of the mid part. The use of three-dimensional face modelling techniques, particularly the mid-face – tear through and cheeks, restores the skin firmness, volume and healthy look. For this purpose the hyaluronic acid is used, calcium hydroxyapatite, and L-polylactic acid fillers. Volumetric techniques require precision and proper selection of the filling agent to give a sense of satisfaction to both the patient and the doctor. PMID:25610354
Multiscale modeling of three-dimensional genome
NASA Astrophysics Data System (ADS)
Zhang, Bin; Wolynes, Peter
The genome, the blueprint of life, contains nearly all the information needed to build and maintain an entire organism. A comprehensive understanding of the genome is of paramount interest to human health and will advance progress in many areas, including life sciences, medicine, and biotechnology. The overarching goal of my research is to understand the structure-dynamics-function relationships of the human genome. In this talk, I will be presenting our efforts in moving towards that goal, with a particular emphasis on studying the three-dimensional organization, the structure of the genome with multi-scale approaches. Specifically, I will discuss the reconstruction of genome structures at both interphase and metaphase by making use of data from chromosome conformation capture experiments. Computationally modeling of chromatin fiber at atomistic level from first principles will also be presented as our effort for studying the genome structure from bottom up.
Three-dimensional modeling equatorial spread F
NASA Astrophysics Data System (ADS)
Huba, J. D.; Krall, J.; Joyce, G.
2008-12-01
Equatorial spread F (ESF) is a low-latitude ionospheric phenomenon that leads to the development of large scale electron density depletions that adversely affect communications and navigation systems. The development of models to understand and predict the onset and evolution of ESF is therefore critically important to a number of space-based systems. To this end, NRL has developed a three-dimensional model of ESF. The global NRL ionosphere model SAMI3 has been modified to simulate a narrow wedge of the post-sunset ionosphere to capture the onset and evolution of ESF. Preliminary results indicate that (1) bubbles can rise to ~ 1600 km, (2) extremely steep ion density gradients can develop in both longitude and latitude, (3) upward plasma velocities approach 1 km/s, and (4) the growth time of the instability is ~eq 15 min. We will also report the effects of meridional and zonal winds on bubble development, as well as ion composition (both atomic and molecular). The simulations will focus on current, low solar activity conditions, and results will be compared to C/NOFS data where available. Research supported by ONR
Magnetocaloric effect in ferroelectric Ising chain magnet
NASA Astrophysics Data System (ADS)
Qi, Yan; Liu, Jia; Yu, Nai-sen; Du, An
2016-05-01
We investigate the magnetocaloric effect (MCE) in multiferroic chain system by adopting the elastic Ising-chain model. Based on the transfer-matrix method, the magnetothermal quantities of characterizing MCE behaviors including the entropy, entropy change and adiabatic cooling rate are rigorously determined. Combined with analysis of ground-state, we mainly discuss results in an antiferromagnetic regime associated with ferroelectric transition. Our results show that the entropy change is greatly enhanced near the saturation field as frustration parameter varies in this regime, and accompanied with remarkable inverse MCE, indicating the enormous potential of multiferroic system in low-temperature refrigeration. Meanwhile we also observe a prominent temperature variation in the isoentropy curves close to zero-temperature ferroelectric transition, but this enhancing MCE signal is very sensitive to the thermal fluctuations, and can be strongly suppressed even under a small temperature.
Ising antiferromagnet on the 2-uniform lattices
NASA Astrophysics Data System (ADS)
Yu, Unjong
2016-08-01
The antiferromagnetic Ising model is investigated on the twenty 2-uniform lattices using the Monte Carlo method based on the Wang-Landau algorithm and the Metropolis algorithm to study the geometric frustration effect systematically. Based on the specific heat, the residual entropy, and the Edwards-Anderson freezing order parameter, the ground states of them were determined. In addition to the long-range-ordered phase and the spin ice phase found in the Archimedean lattices, two more phases were found. The partial long-range order is long-range order with exceptional disordered sites, which give extensive residual entropy. In the partial spin ice phase, the partial freezing phenomenon appears: A majority of sites are frozen without long-range order, but the other sites are fluctuating even at zero temperature. The spin liquid ground state was not found in the 2-uniform lattices.
Quantum annealing correction for random Ising problems
NASA Astrophysics Data System (ADS)
Pudenz, Kristen L.; Albash, Tameem; Lidar, Daniel A.
2015-04-01
We demonstrate that the performance of a quantum annealer on hard random Ising optimization problems can be substantially improved using quantum annealing correction (QAC). Our error correction strategy is tailored to the D-Wave Two device. We find that QAC provides a statistically significant enhancement in the performance of the device over a classical repetition code, improving as a function of problem size as well as hardness. Moreover, QAC provides a mechanism for overcoming the precision limit of the device, in addition to correcting calibration errors. Performance is robust even to missing qubits. We present evidence for a constructive role played by quantum effects in our experiments by contrasting the experimental results with the predictions of a classical model of the device. Our work demonstrates the importance of error correction in appropriately determining the performance of quantum annealers.
New two-dimensional quantum models with shape invariance
Cannata, F.; Ioffe, M. V.; Nishnianidze, D. N.
2011-02-15
Two-dimensional quantum models which obey the property of shape invariance are built in the framework of polynomial two-dimensional supersymmetric quantum mechanics. They are obtained using the expressions for known one-dimensional shape invariant potentials. The constructed Hamiltonians are integrable with symmetry operators of fourth order in momenta, and they are not amenable to the conventional separation of variables.
Critical behavior of a triangular lattice Ising AF/FM bilayer
NASA Astrophysics Data System (ADS)
Žukovič, M.; Bobák, A.
2016-03-01
We study a bilayer Ising spin system consisting of antiferromagnetic (AF) and ferromagnetic (FM) triangular planes, coupled by ferromagnetic exchange interaction, by standard Monte Carlo and parallel tempering methods. The AF/FM bilayer is found to display the critical behavior completely different from both the single FM and AF constituents as well as the FM/FM and AF/AF bilayers. Namely, by finite-size scaling (FSS) analysis we identify at the same temperature a standard Ising transition from the paramagnetic to FM state in the FM plane that induces a ferrimagnetic state with a finite net magnetic moment in the AF plane. At lower temperatures there is another phase transition, that takes place only in the AF plane, to different ferrimagnetic state with spins on two sublattices pointing parallel and on one sublattice antiparallel to the spins on the FM plane. FSS indicates that the corresponding critical exponents are close to the two-dimensional three-state ferromagnetic Potts model values.
NASA Astrophysics Data System (ADS)
Strečka, Jozef
2006-02-01
Effect of uniaxial single-ion anisotropy upon magnetic properties of a mixed spin-1/2 and spin- S ( S⩾1) Ising model on a bathroom tile (4-8) lattice is examined within the framework of an exact star-triangle mapping transformation. Particular attention is focused on the phase diagrams established for several values of the quantum spin number S. It is shown that the mixed-spin bathroom tile lattice exhibits very similar phase boundaries as the mixed-spin honeycomb lattice whose critical points are merely slightly enhanced with respect to the former ones. The influence of uniaxial single-ion anisotropy upon the total magnetization vs. temperature dependence is particularly investigated as well.
NASA Astrophysics Data System (ADS)
Liu, Guangkun; Kaushal, Nitin; Li, Shaozhi; Bishop, Christopher B.; Wang, Yan; Johnston, Steve; Alvarez, Gonzalo; Moreo, Adriana; Dagotto, Elbio
2016-06-01
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), 10.1103/PhysRevLett.112.106405]. In this publication 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. We also study a simplified version of the 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. 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.
Liu, Guangkun; Kaushal, Nitin; Li, Shaozhi; Bishop, Christopher B; Wang, Yan; Johnston, Steve; Alvarez, Gonzalo; Moreo, Adriana; Dagotto, Elbio
2016-06-01
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)PRLTAO0031-900710.1103/PhysRevLett.112.106405]. In this publication 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. We also study a simplified version of the 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. 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. PMID:27415393
Liu, Guangkun; Kaushal, Nitin; Liu, Shaozhi; Bishop, Christopher B.; Wang, Yan; Johnston, Steve; Alvarez, Gonzalo; Moreo, Adriana; Dagotto, Elbio R.
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
Three-Dimensional Tectonic Model of Taiwan
NASA Astrophysics Data System (ADS)
Wu, Francis; Kuo-Chen, Hao; McIntosh, kirk
2014-05-01
We built a three-dimensional model of the interactions of the Eurasian plate (EUP) the Philippine Sea plate (PSP) and the collisional orogen, in and around Taiwan. The model is based on the results of comprehensive, milt-prong TAIGER experiments on land and at sea as well as other existing data. The clockwise rotating PSP moves NWW at ~8 cm/year relative to the Taiwan Strait. Under northern Taiwan the northward subducting PSP terminates near the edge of eastern Taiwan and collides with EUP at in increasing depth toward the north. Mountain building due to collision of EUP and PSP tapers off where the PSP goes below about 60 km. The PSP in the asthenosphere continues to advance NWW-ward. In central Taiwan PSP and EUP collide fully, lithosphere against lithosphere in the upper 60 km or so, leading to significant thickening of the crust to about 55 km on the Central Range side and about 35 km on the Coastal Range/Arc side. In between these "roots" a high velocity rise is found. Although a clear, steep dipping high velocity zone under Central Taiwan is detected, it is found not to be associated with seismicity. In southern Taiwan, mountains form over well-defined, seismically active subduction zone. The upper mantle high velocity anomaly appears to be continues with that under central Taiwan, but here an inclined seismic zone is found. In this area the Luzon Arc has not yet encountered the continental shelf - thus arc-continental collision has not yet occurred. The orogeny here may involve inversion of the subducted South China Sea lithosphere, rifted Eurasian continent, and/or escape of continental material from central Taiwan. GPS and Leveling data reflect well the 3-D plate collision model.
Simple Two-Dimensional Corrections for One-Dimensional Pulse Tube Models
NASA Technical Reports Server (NTRS)
Lee, J. M.; Kittel, P.; Timmerhaus, K. D.; Radebaugh, R.
2004-01-01
One-dimensional oscillating flow models are very useful for designing pulse tubes. They are simple to use, not computationally intensive, and the physical relationship between temperature, pressure and mass flow are easy to understand when used in conjunction with phasor diagrams. They do not possess, however, the ability to directly calculate thermal and momentum diffusion in the direction transverse to the oscillating flow. To account for transverse effects, lumped parameter corrections, which are obtained though experiment, must be used. Or two-dimensional solutions of the differential fluid equations must be obtained. A linear two-dimensional solution to the fluid equations has been obtained. The solution provides lumped parameter corrections for one-dimensional models. The model accounts for heat transfer and shear flow between the gas and the tube. The complex Nusselt number and complex shear wall are useful in describing these corrections, with phase relations and amplitudes scaled with the Prandtl and Valensi numbers. The calculated ratio, a, between a two-dimensional solution of the oscillating temperature and velocity and a one-dimensional solution for the same shows a scales linearly with Va for Va less than 30. In this region alpha less than 0.5, that is, the enthalpy flow calculated with a two-dimensional model is 50% of a calculation using a one-dimensional model. For Va greater than 250, alpha = 0.8, showing that diffusion is still important even when it is confined to a thing layer near the tube wall.
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.
Ising nematic quantum critical point in a metal: a Monte Carlo study
NASA Astrophysics Data System (ADS)
Lederer, Samuel
The Ising nematic quantum critical point (QCP) associated with the zero temperature transition from a symmetric to a nematic metal is an exemplar of metallic quantum criticality. We have carried out a minus sign-free quantum Monte Carlo study of this QCP for a two dimensional lattice model with sizes up to 24 × 24 sites. The system remains non-superconducting down to the lowest accessible temperatures. The results exhibit critical scaling behavior over the accessible ranges of temperature, (imaginary) time, and distance. This scaling behavior has remarkable similarities with recently measured properties of the Fe-based superconductors proximate to their putative nematic QCP. With Yoni Schattner, Steven A. Kivelson, and Erez Berg.
Theory of microwave absorption by the spin-1/2 Heisenberg-Ising magnet.
Brockmann, Michael; Göhmann, Frank; Karbach, Michael; Klümper, Andreas; Weisse, Alexander
2011-07-01
We analyze the problem of microwave absorption by the Heisenberg-Ising magnet in terms of shifted moments of the imaginary part of the dynamical susceptibility. When both the Zeeman field and the wave vector of the incident microwave are parallel to the anisotropy axis, the first four moments determine the shift of the resonance frequency and the linewidth in a situation where the frequency is varied for fixed Zeeman field. For the one-dimensional model we can calculate the moments exactly. This provides exact data for the resonance shift and the linewidth at arbitrary temperatures and magnetic fields. In current ESR experiments the Zeeman field is varied for fixed frequency. We show how in this situation the moments give perturbative results for the resonance shift and for the integrated intensity at small anisotropy as well as an explicit formula connecting the linewidth with the anisotropy parameter in the high-temperature limit. PMID:21797567
Dimensional crossover in a Fermi gas and a cross-dimensional Tomonaga-Luttinger model
NASA Astrophysics Data System (ADS)
Lang, Guillaume; Hekking, Frank; Minguzzi, Anna
2016-01-01
We describe the dimensional crossover in a noninteracting Fermi gas in an anisotropic trap, obtained by populating various transverse modes of the trap. We study the dynamical structure factor and drag force. Starting from a dimension d , the (d +1 ) -dimensional case is obtained to a good approximation with relatively few modes. We show that the dynamical structure factor of a gas in a d -dimensional harmonic trap simulates an effective 2 d -dimensional box trap. We focus then on the experimentally relevant situation when only a portion of the gas in harmonic confinement is probed and give a condition to obtain the behavior of a d -dimensional gas in a box. Finally, we propose a generalized Tomonaga-Luttinger model for the multimode configuration and compare the dynamical structure factor in the two-dimensional limit with the exact result, finding that it is accurate in the backscattering region and at low energy.
Three-Dimensional Lithium-Ion Battery Model (Presentation)
Kim, G. H.; Smith, K.
2008-05-01
Nonuniform battery physics can cause unexpected performance and life degradations in lithium-ion batteries; a three-dimensional cell performance model was developed by integrating an electrode-scale submodel using a multiscale modeling scheme.
Transfer-matrix scaling for diluted Ising systems
NASA Astrophysics Data System (ADS)
de Queiroz, S. L. A.; Stinchcombe, R. B.
1992-09-01
A transfer-matrix scaling technique is developed for randomly diluted systems and applied to the site-diluted Ising model on a square lattice. For each connected configuration between adjacent columns, the contribution of the respective transfer matrix to the decay of correlations is considered only as far as the ratio of the two largest eigenvalues, allowing an economical incorporation of configurational averages. Predictions for the phase boundary at and near the percolation and pure Ising limits, and for the correlation exponent η at those limits, agree with exactly known results to within 1% error with largest strip widths of only L=5. The exponent η remains near the pure value (1/4) for all intermediate concentrations until it turns over to the percolation value at the threshold.
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.
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.
NASA Astrophysics Data System (ADS)
Suzuki, Itsuko S.; Suzuki, Masatsugu
2008-12-01
Cu0.5Co0.5Cl2-FeCl3 graphite bi-intercalation compound is a three-dimensional short-range spin glass with a spin freezing temperature TSG (=3.92±0.11K) . The time evolution of the zero-field-cooled magnetization MZFC(t) has been measured under various combinations of wait time (tw) , temperature (T) , temperature shift (ΔT) , and magnetic field (H) . The relaxation rate SZFC(t) [=(1/H)dMZFC(t)/dlnt] shows a peak at a peak time tcr . The shape of SZFC(t) in the vicinity of tcr is well described by stretched exponential relaxation (SER). The SER exponent b and the SER relaxation time τSER are determined as a function of tw , T , H , and ΔT . The value of b at T=TSG is nearly equal to 0.3. There is a correlation between τSER and 1/b , irrespective of the values of tw , T , H , and ΔT . These features can be well explained in terms of a simple relaxation model for glassy dynamics.
A Five Dimensional Model for Educating the Net Generation
ERIC Educational Resources Information Center
Beyers, Ronald Noel
2009-01-01
This paper proposes a multi-dimensional concept model of an ICT enabled classroom to highlight potential similarities and differences between where teachers perceive themselves relative to their learners. Some teachers and learners may be at the two dimensional text-book level, while others are operating in at a globalization level. Being armed…
Dynamic colloidal assembly pathways via low dimensional models.
Yang, Yuguang; Thyagarajan, Raghuram; Ford, David M; Bevan, Michael A
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 characterized 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. PMID:27250328
Dynamic colloidal assembly pathways via low dimensional models
NASA Astrophysics Data System (ADS)
Yang, Yuguang; Thyagarajan, Raghuram; Ford, David M.; Bevan, Michael A.
2016-05-01
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 characterized 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.
Model of a Negatively Curved Two-Dimensional Space.
ERIC Educational Resources Information Center
Eckroth, Charles A.
1995-01-01
Describes the construction of models of two-dimensional surfaces with negative curvature that are used to illustrate differences in the triangle sum rule for the various Big Bang Theories of the universe. (JRH)
Two-Dimensional Intercomparison of Stratospheric Models
NASA Technical Reports Server (NTRS)
Jackman, Charles H. (Editor); Seals, Robert K., Jr. (Editor); Prather, Michael J. (Editor)
1989-01-01
A detailed record is provided for the examination of fundamental differences in photochemistry and transport among atmospheric models. The results of 16 different modeling groups are presented for several model experiments.
Spectral analysis of two-dimensional Bose-Hubbard models
NASA Astrophysics Data System (ADS)
Fischer, David; Hoffmann, Darius; Wimberger, Sandro
2016-04-01
One-dimensional Bose-Hubbard models are well known to obey a transition from regular to quantum-chaotic spectral statistics. We are extending this concept to relatively simple two-dimensional many-body models. Also in two dimensions a transition from regular to chaotic spectral statistics is found and discussed. In particular, we analyze the dependence of the spectral properties on the bond number of the two-dimensional lattices and the applied boundary conditions. For maximal connectivity, the systems behave most regularly in agreement with the applicability of mean-field approaches in the limit of many nearest-neighbor couplings at each site.
Roaming form factors for the tricritical to critical Ising flow
NASA Astrophysics Data System (ADS)
Horváth, D. X.; Dorey, P. E.; Takács, G.
2016-07-01
We study the massless flows described by the staircase model introduced by Al.B. Zamolodchikov through the analytic continuation of the sinh-Gordon S-matrix, focusing on the renormalisation group flow from the tricritical to the critical Ising model. We show that the properly defined roaming limits of certain sinh-Gordon form factors are identical to the form factors of the order and disorder operators for the massless flow. As a by-product, we also construct form factors for a semi-local field in the sinh-Gordon model, which can be associated with the twist field in the ultraviolet limiting free massless bosonic theory.
Three Dimensional Vapor Intrusion Modeling: Model Validation and Uncertainty Analysis
NASA Astrophysics Data System (ADS)
Akbariyeh, S.; Patterson, B.; Rakoczy, A.; Li, Y.
2013-12-01
Volatile organic chemicals (VOCs), such as chlorinated solvents and petroleum hydrocarbons, are prevalent groundwater contaminants due to their improper disposal and accidental spillage. In addition to contaminating groundwater, VOCs may partition into the overlying vadose zone and enter buildings through gaps and cracks in foundation slabs or basement walls, a process termed vapor intrusion. Vapor intrusion of VOCs has been recognized as a detrimental source for human exposures to potential carcinogenic or toxic compounds. The simulation of vapor intrusion from a subsurface source has been the focus of many studies to better understand the process and guide field investigation. While multiple analytical and numerical models were developed to simulate the vapor intrusion process, detailed validation of these models against well controlled experiments is still lacking, due to the complexity and uncertainties associated with site characterization and soil gas flux and indoor air concentration measurement. In this work, we present an effort to validate a three-dimensional vapor intrusion model based on a well-controlled experimental quantification of the vapor intrusion pathways into a slab-on-ground building under varying environmental conditions. Finally, a probabilistic approach based on Monte Carlo simulations is implemented to determine the probability distribution of indoor air concentration based on the most uncertain input parameters.
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.
The Long Decay Model of One-Dimensional Projectile Motion
ERIC Educational Resources Information Center
Lattery, Mark Joseph
2008-01-01
This article introduces a research study on student model formation and development in introductory mechanics. As a point of entry, I present a detailed analysis of the Long Decay Model of one-dimensional projectile motion. This model has been articulated by Galileo ("in De Motu") and by contemporary students. Implications for instruction are…
The Hidden Symmetries of Spin-1 Ising Lattice Gas for Usual Quantum Hamiltonians
NASA Astrophysics Data System (ADS)
Payandeh, Farrin
2016-02-01
In this letter, the most common quantum Hamiltonian is exploited in order to compare the definite equivalences, corresponding to possible spin values in a lattice gas model, to those in a spin-1 Ising model. Our approach also requires interpolating both results in a p-state clock model, in order to find the hidden symmetries of both under consideration models.
Nonminimal universal extra dimensional model confronts Bs→μ+μ-
NASA Astrophysics Data System (ADS)
Datta, Anindya; Shaw, Avirup
2016-03-01
The addition of boundary localized kinetic and Yukawa terms to the action of a five-dimensional Standard Model would nontrivially modify the Kaluza-Klein spectra and some of the interactions among the Kaluza-Klein excitations compared to the minimal version of this model, in which these boundary terms are not present. In the minimal version of this framework, known as the universal extra dimensional model, special assumptions are made about these unknown, beyond the cutoff contributions to restrict the number of unknown parameters of the theory to be minimum. We estimate the contribution of Kaluza-Klein modes to the branching ratios of Bs (d )→μ+μ- in the framework of the nonminimal universal extra dimensional model, at one-loop level. The results have been compared to the experimental data to constrain the parameters of this model. From the measured decay branching ratio of Bs→μ+μ- (depending on the values of boundary localized parameters), the lower limit on R-1 can be as high as 800 GeV. We have briefly reviewed the bounds on nonminimal universal extra dimensional parameter space coming from electroweak precision observables. The present analysis (Bs→μ+μ-) has ruled out new regions of parameter space in comparison to the analysis of electroweak data. We have revisited the bound on R-1 in the universal extra dimensional model, which came out to be 454 GeV. This limit on R-1 in the universal extra dimensional framework is not as competitive as the limits derived from the consideration of relic density or Standard Model Higgs boson production and decay to W+W-. Unfortunately, the Bd→μ+μ- decay branching ratio would not set any significant limit on R-1 in a minimal or nonminimal universal extra dimensional model.
Three-dimensional hydrodynamic modeling of a bubbling fluidized bed
Gamwo, I.K.; Soong, Y.; Gidaspow, D.; Lyczkowski, R.W.
1995-12-31
A well-posed three-dimensional model for bed dynamics was developed starting from an ill-posed model. The new model has predicted a roughly-spheroidal bubble shape and computed porosity distributions consistent with experimental observations with no disturbing ``fountain`` as predicted by the earlier model. The model can be applied to a variety of gas-solids flows of practical interest such as fluidization, pneumatic conveying, and two-phase jets, as well as liquid-solids flows.
Transition modes in Ising networks: an approximate theory for macromolecular recognition.
Keating, S; Di Cera, E
1993-01-01
For a statistical lattice, or Ising network, composed of N identical units existing in two possible states, 0 and 1, and interacting according to a given geometry, a set of values can be found for the mean free energy of the 0-->1 transition of a single unit. Each value defines a transition mode in an ensemble of nu N = 3N - 2N possible values and reflects the role played by intermediate states in shaping the energetics of the system as a whole. The distribution of transition modes has a number of intriguing properties. Some of them apply quite generally to any Ising network, regardless of its dimension, while others are specific for each interaction geometry and dimensional embedding and bear on fundamental aspects of analytical number theory. The landscape of transition modes encapsulates all of the important thermodynamic properties of the network. The free energy terms defining the partition function of the system can be derived from the modes by simple transformations. Classical mean-field expressions can be obtained from consideration of the properties of transition modes in a rather straightforward way. The results obtained in the analysis of the transition mode distributions have been used to develop an approximate treatment of the problem of macromolecular recognition. This phenomenon is modeled as a cooperative process that involves a number of recognition subsites across an interface generated by the binding of two macromolecular components. The distribution of allowed binding free energies for the system is shown to be a superposition of Gaussian terms with mean and variance determined a priori by the theory. Application to the analysis of the biologically interaction of thrombin with hirudin has provided some useful information on basic aspects of the interaction, such as the number of recognition subsites involved and the energy balance for binding and cooperative coupling among them. Our results agree quite well with information derived independently
Numerical modeling of two-dimensional confined flows
NASA Technical Reports Server (NTRS)
Greywall, M. S.
1979-01-01
A numerical model of two-dimensional confined flows is presented. The flow in the duct is partitioned into finite streams. The difference equations are then obtained by applying conservation principles directly to the individual streams. A listing of a computer code based on this approach in FORTRAN 4 language is presented. The code computes two dimensional compressible turbulent flows in ducts when the duct area along the flow is specified and the pressure gradient is unknown.
Response characteristics of a low-dimensional model neuron.
Cartling, B
1996-11-15
It is shown that a low-dimensional model neuron with a response time constant smaller than the membrane time constant closely reproduces the activity and excitability behavior of a detailed conductance-based model of Hodgkin-Huxley type. The fast response of the activity variable also makes it possible to reduce the model to a one-dimensional model, in particular for typical conditions. As an example, the reduction to a single-variable model from a multivariable conductance-based model of a neocortical pyramidal cell with somatic input is demonstrated. The conditions for avoiding a spurious damped oscillatory response to a constant input are derived, and it is shown that a limit-cycle response cannot occur. The capability of the low-dimensional model to approximate higher-dimensional models accurately makes it useful for describing complex dynamics of nets of interconnected neurons. The simplicity of the model facilitates analytic studies, elucidations of neurocomputational mechanisms, and applications to large-scale systems. PMID:8888611
A two-dimensional dam-break flood plain model
Hromadka, T.V., II; Berenbrock, C.E.; Freckleton, J.R.; Guymon, G.L.
1985-01-01
A simple two-dimensional dam-break model is developed for flood plain study purposes. Both a finite difference grid and an irregular triangle element integrated finite difference formulation are presented. The governing flow equations are approximately solved as a diffusion model coupled to the equation of continuity. Application of the model to a hypothetical dam-break study indicates that the approach can be used to predict a two-dimensional dam-break flood plain over a broad, flat plain more accurately than a one-dimensional model, especially when the flow can break-out of the main channel and then return to the channel at other downstream reaches. ?? 1985.
One-dimensional hydrodynamic model generating a turbulent cascade
NASA Astrophysics Data System (ADS)
Matsumoto, Takeshi; Sakajo, Takashi
2016-05-01
As a minimal mathematical model generating cascade analogous to that of the Navier-Stokes turbulence in the inertial range, we propose a one-dimensional partial-differential-equation model that conserves the integral of the squared vorticity analog (enstrophy) in the inviscid case. With a large-scale random forcing and small viscosity, we find numerically that the model exhibits the enstrophy cascade, the broad energy spectrum with a sizable correction to the dimensional-analysis prediction, peculiar intermittency, and self-similarity in the dynamical system structure.
Multi-Scale Multi-Dimensional Ion Battery Performance Model
2007-05-07
The Multi-Scale Multi-Dimensional (MSMD) Lithium Ion Battery Model allows for computer prediction and engineering optimization of thermal, electrical, and electrochemical performance of lithium ion cells with realistic geometries. The model introduces separate simulation domains for different scale physics, achieving much higher computational efficiency compared to the single domain approach. It solves a one dimensional electrochemistry model in a micro sub-grid system, and captures the impacts of macro-scale battery design factors on cell performance and materialmore » usage by solving cell-level electron and heat transports in a macro grid system.« less
Low-dimensional supersymmetric lattice models
Bergner, G. Kaestner, T. Uhlmann, S. Wipf, A.
2008-04-15
We study and simulate N=2 supersymmetric Wess-Zumino models in one and two dimensions. For any choice of the lattice derivative, the theories can be made manifestly supersymmetric by adding appropriate improvement terms corresponding to discretizations of surface integrals. In one dimension, our simulations show that a model with the Wilson derivative and the Stratonovich prescription for this discretization leads to far better results at finite lattice spacing than other models with Wilson fermions considered in the literature. In particular, we check that fermionic and bosonic masses coincide and the unbroken Ward identities are fulfilled to high accuracy. Equally good results for the effective masses can be obtained in a model with the SLAC derivative (even without improvement terms). In two dimensions we introduce a non-standard Wilson term in such a way that the discretization errors of the kinetic terms are only of order O(a{sup 2}). Masses extracted from the corresponding manifestly supersymmetric model prove to approach their continuum values much quicker than those from a model containing the standard Wilson term. Again, a comparable enhancement can be achieved in a theory using the SLAC derivative.
Large field inflation models from higher-dimensional gauge theories
NASA Astrophysics Data System (ADS)
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-01
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante's Inferno model turns out to be the most preferred model in this framework.
Spatial and Temporal Low-Dimensional Models for Fluid Flow
NASA Technical Reports Server (NTRS)
Kalb, Virginia
2008-01-01
A document discusses work that obtains a low-dimensional model that captures both temporal and spatial flow by constructing spatial and temporal four-mode models for two classic flow problems. The models are based on the proper orthogonal decomposition at two reference Reynolds numbers. Model predictions are made at an intermediate Reynolds number and compared with direct numerical simulation results at the new Reynolds number.
Large field inflation models from higher-dimensional gauge theories
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-23
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante’s Inferno model turns out to be the most preferred model in this framework.
Multi-dimensional Indoor Location Information Model
NASA Astrophysics Data System (ADS)
Xiong, Q.; Zhu, Q.; Zlatanova, S.; Huang, L.; Zhou, Y.; Du, Z.
2013-11-01
Aiming at the increasing requirements of seamless indoor and outdoor navigation and location service, a Chinese standard of Multidimensional Indoor Location Information Model is being developed, which defines ontology of indoor location. The model is complementary to 3D concepts like CityGML and IndoorGML. The goal of the model is to provide an exchange GML-based format for location needed for indoor routing and navigation. An elaborated user requirements analysis and investigation of state-of-the-art technology in expressing indoor location at home and abroad was completed to identify the manner humans specify location. The ultimate goal is to provide an ontology that will allow absolute and relative specification of location such as "in room 321", "on the second floor", as well as, "two meters from the second window", "12 steps from the door".
Quasicrystal Ising chain and automata theory
Allouche, J.P.; France, M.M.
1986-03-01
An automatic sequence is generated by a finite machine (automaton). These sequences can be periodic or not; in the latter case, however, they are not random, but rather ''quasicrystalline.'' The authors consider an Ising chain with variable interaction in a uniform external field, at zero temperature, and prove that, if this interaction is automatic, then the induced magnetic field is also automatic.
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.
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.
Underwater striling engine design with modified one-dimensional model
NASA Astrophysics Data System (ADS)
Li, Daijin; Qin, Kan; Luo, Kai
2015-05-01
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.
Two-dimensional charge-control model for MODFET's
NASA Astrophysics Data System (ADS)
Kim, Young Min; Roblin, Patrick
1986-11-01
A dc model for MODFET's accounting for two-dimensional effects is proposed. In this model, charge control is realized by solving the two-dimensional Poisson equation in the depleted AlGaAs region. The transport picture used for the two-dimensional electron gas (2-DEG) in the AlGaAs/GaAs heterojunction relies on the quasi-Fermi level together with a field-dependent mobility and therefore includes 2-DEG diffusion effects. The approach reduces the analysis to a single integral equation. I-V curves, which provide a good fitting to the reported experimental data, are obtained using a smooth velocity-field curve. The channel voltage, 2-DEG concentration, parallel electric-field, and drift velocity along the channel are given in this study and provide a clear picture of current saturation. The model is consistent with the approximate two-region saturation picture but provides a smoother transition.
SKRYN: A fast semismooth-Krylov-Newton method for controlling Ising spin systems
NASA Astrophysics Data System (ADS)
Ciaramella, G.; Borzì, A.
2015-05-01
The modeling and control of Ising spin systems is of fundamental importance in NMR spectroscopy applications. In this paper, two computer packages, ReHaG and SKRYN, are presented. Their purpose is to set-up and solve quantum optimal control problems governed by the Liouville master equation modeling Ising spin-1/2 systems with pointwise control constraints. In particular, the MATLAB package ReHaG allows to compute a real matrix representation of the master equation. The MATLAB package SKRYN implements a new strategy resulting in a globalized semismooth matrix-free Krylov-Newton scheme. To discretize the real representation of the Liouville master equation, a norm-preserving modified Crank-Nicolson scheme is used. Results of numerical experiments demonstrate that the SKRYN code is able to provide fast and accurate solutions to the Ising spin quantum optimization problem.
Three-dimensional model for fusion processes
Olson, A.P.
1984-01-01
Active galactic nuclei (AGN) emit unusual spectra of radiation which is interpreted to signify extreme distance, extreme power, or both. The status of AGNs was recently reviewed by Balick and Heckman. It seems that the greatest conceptual difficulty with understanding AGNs is how to form a coherent phenomenological model of their properties. What drives the galactic engine. What and where are the mass-flows of fuel to this engine. Are there more than one engine. Do the engines have any symmetry properties. Is observed radiation isotropically emitted from the source. If it is polarized, what causes the polarization. Why is there a roughly spherical cloud of ionized gas about the center of our own galaxy, the Milky Way. The purpose of this paper is to discuss a new model, based on fusion processes which are not axisymmetric, uniform, isotropic, or even time-invariant. Then, the relationship to these questions will be developed. A unified model of fusion processes applicable to many astronomical phenomena will be proposed and discussed.
Semi-Empirical Modeling of Two-Dimensional and Three-Dimensional Dynamic Stall
NASA Astrophysics Data System (ADS)
Modarres, Ramin
Helicopters are generally limited in their performance by the phenomenon of dynamic stall. The purpose of this work is to develop a method for modeling dynamic stall that is appropriate to preliminary design and flight simulator applications. Unlike other semi-empirical dynamic stall models, the model developed in this thesis, not only counts for the well-known, three-dimensional flow effects on the stalled loads but also captures the secondary vortex-shedding phenomenon that has been seen in experiments. The fundamental physics that modify dynamic-stall behavior and that have been extended from two-dimensional to three-dimensional flow are, namely: 1.) yawed flow, 2.) time-varying velocity, 3.) the rotational environment and 4.) the radial blade coupling. For the reduced-order modeling, extra nonlinear states have been added to the dynamic stall model in order to simulate the double-dynamic-stall phenomenon. The results of this study will have practical applications to aerospace systems, such as compliant or morphing surfaces in rotary-wing systems that encounter transient or periodic separation and reattachment during phenomena such as dynamic stall.
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
Fermions in five-dimensional brane world models
NASA Astrophysics Data System (ADS)
Smolyakov, Mikhail N.
2016-06-01
In the present paper the fermion fields, living in the background of five-dimensional warped brane world models with compact extra dimension, are thoroughly examined. The Kaluza-Klein decomposition and isolation of the physical degrees of freedom is performed for those five-dimensional fermion field Lagrangians, which admit such a decomposition to be performed in a mathematically consistent way and provide a physically reasonable four-dimensional effective theory. It is also shown that for the majority of five-dimensional fermion field Lagrangians there are no (at least rather obvious) ways to perform the Kaluza-Klein decomposition consistently. Moreover, in these cases one may expect the appearance of various pathologies in the four-dimensional effective theory. Among the cases, for which the Kaluza-Klein decomposition can be performed in a mathematically consistent way, the case, which reproduces the Standard Model by the zero Kaluza-Klein modes most closely regardless of the size of the extra dimension, is examined in detail in the background of the Randall-Sundrum model.
Finite-temperature scaling at the quantum critical point of the Ising chain in a transverse field
NASA Astrophysics Data System (ADS)
Haelg, Manuel; Huvonen, Dan; Guidi, Tatiana; Quintero-Castro, Diana Lucia; Boehm, Martin; Regnault, Louis-Pierre; Zheludev, Andrey
2015-03-01
Inelastic neutron scattering is used to study the finite-temperature scaling behavior of spin correlations at the quantum critical point in an experimental realization of the one-dimensional Ising model in a transverse field. The target compound is the well-characterized, anisotropic and bond-alternating Heisenberg spin-1 chain material NTENP. The validity and the limitations of the dynamic structure factor scaling are tested, discussed and compared to theoretical predictions. For this purpose neutron data have been collected on the three-axes spectrometers IN14 at ILL and FLEXX at HZB as well as on the time of flight multi-chopper spectrometer LET at ISIS. In addition to the general statement about quantum criticality and universality, present study also reveals new insight into the properties of the spin chain compound NTENP in particular.
Three-dimensional models. [For orbital celestial mechanics
Hunter, C. )
1990-06-01
The Schwarzschild (1979) approach to the analysis of three-dimensional galactic models is reviewed. An analysis of triaxial Staeckel models is discussed which shows that such models have a wide variety of possible distribution functions. The uniqueness that Schwarzschild first encountered in his discrete formulation of the problem of finding a three-integral distribution function for a triaxial density is real and not an artifact of the finite cell approximation. 27 refs.
On numerical modeling of one-dimensional geothermal histories
Haugerud, R.A.
1989-01-01
Numerical models of one-dimensional geothermal histories are one way of understanding the relations between tectonics and transient thermal structure in the crust. Such models can be powerful tools for interpreting geochronologic and thermobarometric data. A flexible program to calculate these models on a microcomputer is available and examples of its use are presented. Potential problems with this approach include the simplifying assumptions that are made, limitations of the numerical techniques, and the neglect of convective heat transfer. ?? 1989.
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.
Midlatitude Pi2 pulsations: AFGL and ISEE magnetometer observations correlated
Hughes, W.J.; Singer, H.J.; Maynard, N.C.
1982-01-01
The ISEE observations of the pi2 magnetic pulsations occuring substorm onset in the inner magnetosphere are discussed. One of these events which was also detected as a pi2 event by the AFGL midlatitude magnetometers is considered. The event occurred when the foot of the ISEE field line was over North America. The ground and satellite signals are remarkably similar: they start and stop at the same time, have the same period and can be correlated cycle by cycle. The waves are detected in the electric field data from ISEE 1 and in the magnetic field data from both ISEE 1 and ISEE 2. Calculation of the Poynting vector at ISEE 1 shows that the energy flowed mainly westward, but that there was also a component towards the nearer (southern) ionospheric foot of the field line. The phases between the various field components measured by ISEE 1 and 2 indicate that this is a standing hydromagnetic oscillation.
Programmers manual for a one-dimensional Lagrangian transport model
Schoellhamer, D.H.; Jobson, H.E.
1986-01-01
A one-dimensional Lagrangian transport model for simulating water-quality constituents such as temperature, dissolved oxygen , and suspended sediment in rivers is presented in this Programmers Manual. Lagrangian transport modeling techniques, the model 's subroutines, and the user-written decay-coefficient subroutine are discussed in detail. Appendices list the program codes. The Programmers Manual is intended for the model user who needs to modify code either to adapt the model to a particular need or to use reaction kinetics not provided with the model. (Author 's abstract)
Evaluation of one dimensional analytical models for vegetation canopies
NASA Technical Reports Server (NTRS)
Goel, Narendra S.; Kuusk, Andres
1992-01-01
The SAIL model for one-dimensional homogeneous vegetation canopies has been modified to include the specular reflectance and hot spot effects. This modified model and the Nilson-Kuusk model are evaluated by comparing the reflectances given by them against those given by a radiosity-based computer model, Diana, for a set of canopies, characterized by different leaf area index (LAI) and leaf angle distribution (LAD). It is shown that for homogeneous canopies, the analytical models are generally quite accurate in the visible region, but not in the infrared region. For architecturally realistic heterogeneous canopies of the type found in nature, these models fall short. These shortcomings are quantified.
Predicting bite force in mammals: two-dimensional versus three-dimensional lever models.
Davis, J L; Santana, S E; Dumont, E R; Grosse, I R
2010-06-01
Bite force is a measure of whole-organism performance that is often used to investigate the relationships between performance, morphology and fitness. When in vivo measurements of bite force are unavailable, researchers often turn to lever models to predict bite forces. This study demonstrates that bite force predictions based on two-dimensional (2-D) lever models can be improved by including three-dimensional (3-D) geometry and realistic physiological cross-sectional areas derived from dissections. Widely used, the 2-D method does a reasonable job of predicting bite force. However, it does so by over predicting physiological cross-sectional areas for the masseter and pterygoid muscles and under predicting physiological cross-sectional areas for the temporalis muscle. We found that lever models that include the three dimensional structure of the skull and mandible and physiological cross-sectional areas calculated from dissected muscles provide the best predictions of bite force. Models that accurately represent the biting mechanics strengthen our understanding of which variables are functionally relevant and how they are relevant to feeding performance. PMID:20472771
Likelihood-Free Inference in High-Dimensional Models.
Kousathanas, Athanasios; Leuenberger, Christoph; Helfer, Jonas; Quinodoz, Mathieu; Foll, Matthieu; Wegmann, Daniel
2016-06-01
Methods that bypass analytical evaluations of the likelihood function have become an indispensable tool for statistical inference in many fields of science. These so-called likelihood-free methods rely on accepting and rejecting simulations based on summary statistics, which limits them to low-dimensional models for which the value of the likelihood is large enough to result in manageable acceptance rates. To get around these issues, we introduce a novel, likelihood-free Markov chain Monte Carlo (MCMC) method combining two key innovations: updating only one parameter per iteration and accepting or rejecting this update based on subsets of statistics approximately sufficient for this parameter. This increases acceptance rates dramatically, rendering this approach suitable even for models of very high dimensionality. We further derive that for linear models, a one-dimensional combination of statistics per parameter is sufficient and can be found empirically with simulations. Finally, we demonstrate that our method readily scales to models of very high dimensionality, using toy models as well as by jointly inferring the effective population size, the distribution of fitness effects (DFE) of segregating mutations, and selection coefficients for each locus from data of a recent experiment on the evolution of drug resistance in influenza. PMID:27052569
Emergent friction in two-dimensional Frenkel-Kontorova models
NASA Astrophysics Data System (ADS)
Norell, Jesper; Fasolino, Annalisa; de Wijn, Astrid S.
2016-08-01
Simple models for friction are typically one-dimensional, but real interfaces are two-dimensional. We investigate the effects of the second dimension on static and dynamic friction by using the Frenkel-Kontorova (FK) model. We study the two most straightforward extensions of the FK model to two dimensions and simulate both the static and dynamic properties. We show that the behavior of the static friction is robust and remains similar in two dimensions for physically reasonable parameter values. The dynamic friction, however, is strongly influenced by the second dimension and the accompanying additional dynamics and parameters introduced into the models. We discuss our results in terms of the thermal equilibration and phonon dispersion relations of the lattices, establishing a physically realistic and suitable two-dimensional extension of the FK model. We find that the presence of additional dissipation channels can increase the friction and produces significantly different temperature dependence when compared to the one-dimensional case. We also briefly study the anisotropy of the dynamic friction and show highly nontrivial effects, including that the friction anisotropy can lead to motion in different directions depending on the value of the initial velocity.
Local properties of the two-dimensional Hubbard model
NASA Astrophysics Data System (ADS)
Drewes, Jan; Miller, Luke; Cocchi, Eugenio; Chan, Chun Fai; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael
2016-05-01
Quantum gases of interacting fermionic atoms in optical lattices promise to shed new light on the low-temperature phases of the Hubbard model such as spin-ordered phases, or in particular, on possible d-wave superconductivity. In this context it remains challenging to further reduce the temperature of the trapped gas. We experimentally realize the two-dimensional Hubbard model by loading a quantum degenerate Fermi gas of 40K atoms into a three-dimensional optical lattice geometry. By tuning the interaction between the two lowest hyperfine states to strong repulsion the two-dimensional Mott-insulator is created. High resolution absorption imaging in combination with radio-frequency spectroscopy is applied to spatially resolve the atomic distribution in a single layer in the vertical direction. This measurement scheme gives direct access to the local properties of the trapped gas and we present most recent data on the distribution of entropy and density-density fluctuations.
Brane compactifications and 4-dimensional geometry in the IKKT model
NASA Astrophysics Data System (ADS)
Polychronakos, Alexios P.; Steinacker, Harold; Zahn, Jochen
2013-10-01
We study in detail certain brane solutions with compact extra dimensions M4×K in the IKKT matrix model, with K being a two-dimensional rotating torus embedded in R6. We focus on the compactification moduli and the fluctuations of K⊂R6 and their physical significance. Mediated by the Poisson tensor, they contribute to the effective 4-dimensional metric on the brane, and thereby become gravitational degrees of freedom. We show that the zero modes corresponding to the global symmetries of the model lead to Ricci-flat 4-dimensional metric perturbations, wherever the energy-momentum tensor vanishes. Their coupling to the energy-momentum tensor depends on the extrinsic curvature of the brane.
Micropolar continuum modelling of bi-dimensional tetrachiral lattices
Chen, Y.; Liu, X. N.; Hu, G. K.; Sun, Q. P.; Zheng, Q. S.
2014-01-01
The in-plane behaviour of tetrachiral lattices should be characterized by bi-dimensional orthotropic material owing to the existence of two orthogonal axes of rotational symmetry. Moreover, the constitutive model must also represent the chirality inherent in the lattices. To this end, a bi-dimensional orthotropic chiral micropolar model is developed based on the theory of irreducible orthogonal tensor decomposition. The obtained constitutive tensors display a hierarchy structure depending on the symmetry of the underlying microstructure. Eight additional material constants, in addition to five for the hemitropic case, are introduced to characterize the anisotropy under Z2 invariance. The developed continuum model is then applied to a tetrachiral lattice, and the material constants of the continuum model are analytically derived by a homogenization process. By comparing with numerical simulations for the discrete lattice, it is found that the proposed continuum model can correctly characterize the static and wave properties of the tetrachiral lattice. PMID:24808754
Novak, Gregory S.; Ostriker, Jeremiah P.; Ciotti, Luca
2011-08-10
We extend the black hole (BH) feedback models of Ciotti, Ostriker, and Proga to two dimensions. In this paper, we focus on identifying the differences between the one-dimensional and two-dimensional hydrodynamical simulations. We examine a normal, isolated L{sub *} galaxy subject to the cooling flow instability of gas in the inner regions. Allowance is made for subsequent star formation, Type Ia and Type II supernovae, radiation pressure, and inflow to the central BH from mildly rotating galactic gas which is being replenished as a normal consequence of stellar evolution. The central BH accretes some of the infalling gas and expels a conical wind with mass, momentum, and energy flux derived from both observational and theoretical studies. The galaxy is assumed to have low specific angular momentum in analogy with the existing one-dimensional case in order to isolate the effect of dimensionality. The code then tracks the interaction of the outflowing radiation and winds with the galactic gas and their effects on regulating the accretion. After matching physical modeling to the extent possible between the one-dimensional and two-dimensional treatments, we find essentially similar results in terms of BH growth and duty cycle (fraction of the time above a given fraction of the Eddington luminosity). In the two-dimensional calculations, the cool shells forming at 0.1-1 kpc from the center are Rayleigh-Taylor unstable to fragmentation, leading to a somewhat higher accretion rate, less effective feedback, and a more irregular pattern of bursting compared with the one-dimensional case.
NASA Astrophysics Data System (ADS)
Wang, Hai Tao; Cho, Sam Young
2015-01-01
In order to investigate the quantum phase transition in the one-dimensional quantum compass model, we numerically calculate non-local string correlations, entanglement entropy and fidelity per lattice site by using the infinite matrix product state representation with the infinite time evolving block decimation method. In the whole range of the interaction parameters, we find that four distinct string orders characterize the four different Haldane phases and the topological quantum phase transition occurs between the Haldane phases. The critical exponents of the string order parameters β = 1/8 and the cental charges c = 1/2 at the critical points show that the topological phase transitions between the phases belong to an Ising type of universality classes. In addition to the string order parameters, the singularities of the second derivative of the ground state energies per site, the continuous and singular behaviors of the Von Neumann entropy and the pinch points of the fidelity per lattice site manifest that the phase transitions between the phases are of the second-order, in contrast to the first-order transition suggested in previous studies.
Wang, Hai Tao; Cho, Sam Young
2015-01-14
In order to investigate the quantum phase transition in the one-dimensional quantum compass model, we numerically calculate non-local string correlations, entanglement entropy and fidelity per lattice site by using the infinite matrix product state representation with the infinite time evolving block decimation method. In the whole range of the interaction parameters, we find that four distinct string orders characterize the four different Haldane phases and the topological quantum phase transition occurs between the Haldane phases. The critical exponents of the string order parameters β = 1/8 and the cental charges c = 1/2 at the critical points show that the topological phase transitions between the phases belong to an Ising type of universality classes. In addition to the string order parameters, the singularities of the second derivative of the ground state energies per site, the continuous and singular behaviors of the Von Neumann entropy and the pinch points of the fidelity per lattice site manifest that the phase transitions between the phases are of the second-order, in contrast to the first-order transition suggested in previous studies. PMID:25478955
Three dimensional global modeling of atmospheric CO2
NASA Technical Reports Server (NTRS)
Fung, I.; Hansen, J.; Rind, D.
1983-01-01
A model was developed to study the prospects of extracting information on carbon dioxide sources and sinks from observed CO2 variations. The approach uses a three dimensional global transport model, based on winds from a 3-D general circulation model (GCM), to advect CO2 noninteractively, i.e., as a tracer, with specified sources and sinks of CO2 at the surface. The 3-D model employed is identified and biosphere, ocean and fossil fuel sources and sinks are discussed. Some preliminary model results are presented.
A Framework for Dimensionality Assessment for Multidimensional Item Response Models
ERIC Educational Resources Information Center
Svetina, Dubravka; Levy, Roy
2014-01-01
A framework is introduced for considering dimensionality assessment procedures for multidimensional item response models. The framework characterizes procedures in terms of their confirmatory or exploratory approach, parametric or nonparametric assumptions, and applicability to dichotomous, polytomous, and missing data. Popular and emerging…
Three dimensional geometric modeling of processing-tomatoes
Technology Transfer Automated Retrieval System (TEKTRAN)
Characterizing tomato geometries with different shapes and sizes would facilitate the design of tomato processing equipments and promote computer-based engineering simulations. This research sought to develop a three-dimensional geometric model that can describe the morphological attributes of proce...
Judgment Research and the Dimensional Model of Personality
ERIC Educational Resources Information Center
Garb, Howard N.
2008-01-01
Comments on the original article "Plate tectonics in the classification of personality disorder: Shifting to a dimensional model," by T. A. Widiger and T. J. Trull. The purpose of this comment is to address (a) whether psychologists know how personality traits are currently assessed by clinicians and (b) the reliability and validity of those…
A two-dimensional analytical model of petroleum vapor intrusion
NASA Astrophysics Data System (ADS)
Yao, Yijun; Verginelli, Iason; Suuberg, Eric M.
2016-02-01
In this study we present an analytical solution of a two-dimensional petroleum vapor intrusion model, which incorporates a steady-state diffusion-dominated vapor transport in a homogeneous soil and piecewise first-order aerobic biodegradation limited by oxygen availability. This new model can help practitioners to easily generate two-dimensional soil gas concentration profiles for both hydrocarbons and oxygen and estimate hydrocarbon indoor air concentrations as a function of site-specific conditions such as source strength and depth, reaction rate constant, soil characteristics and building features. The soil gas concentration profiles generated by this new model are shown in good agreement with three-dimensional numerical simulations and two-dimensional measured soil gas data from a field study. This implies that for cases involving diffusion dominated soil gas transport, steady state conditions and homogenous source and soil, this analytical model can be used as a fast and easy-to-use risk screening tool by replicating the results of 3-D numerical simulations but with much less computational effort.
THREE-DIMENSIONAL NAPL FATE AND TRANSPORT MODEL
We have added several new and significant capabilities to UTCHEM to make it into a general-purpose NAPL simulator. The simulator is now capable of modeling transient and steady-state three-dimensional flow and mass transport in the groundwater (saturated) and vadose (unsaturated...
A Five Dimensional Model for Teaching an Ethnic Content Course.
ERIC Educational Resources Information Center
Curiel, Herman; Euwing, Ella
A model suitable for use in a required social work course or a high-interest elective social work course on ethnic groups, racism, or cross cultural studies uses a five dimensional approach. An elective course entitled "Cultural Diversity and the Helping Process" provides a case study. This course has been taught since 1981 and has occasionally…
Interactive Multimedia and Concrete Three-Dimensional Modelling.
ERIC Educational Resources Information Center
Baxter, J. H.; Preece, Peter F. W.
1999-01-01
Compares a multimedia package for teaching about the phases of the moon to grade 8 (12-year-old) students with a conventional three-dimensional modeling approach. Results show both methods were equally effective in terms of student learning, for male and female students, and prior computer experience was not a factor in multimedia use. (Author/LRW)
Mixed spin-5/2 and spin-2 Ising ferrimagnetic system on the Bethe lattice
NASA Astrophysics Data System (ADS)
Masrour, R.; Jabar, A.; Benyoussef, A.; Hamedoun, M.
2015-11-01
The magnetic properties of spins-S and σ Ising model on the Bethe lattice have been investigated by using the Monte Carlo simulation. The thermal total magnetization and magnetization of spins S and σ with the different exchange interactions, different external magnetic field and different temperatures have been studied. The critical temperature and compensation temperature have been deduced. The magnetic hysteresis cycle of Ising ferrimagnetic system on the Bethe lattice has been deduced for different values of exchange interactions between the spins S and σ, for different values of crystal field and for different sizes. The magnetic coercive filed has been deduced.
One-dimensional XY model: Ergodic properties and hydrodynamic limit
NASA Astrophysics Data System (ADS)
Shuhov, A. G.; Suhov, Yu. M.
1986-11-01
We prove theorems on convergence to a stationary state in the course of time for the one-dimensional XY model and its generalizations. The key point is the well-known Jordan-Wigner transformation, which maps the XY dynamics onto a group of Bogoliubov transformations on the CAR C *-algebra over Z 1. The role of stationary states for Bogoliubov transformations is played by quasifree states and for the XY model by their inverse images with respect to the Jordan-Wigner transformation. The hydrodynamic limit for the one-dimensional XY model is also considered. By using the Jordan-Wigner transformation one reduces the problem to that of constructing the hydrodynamic limit for the group of Bogoliubov transformations. As a result, we obtain an independent motion of "normal modes," which is described by a hyperbolic linear differential equation of second order. For the XX model this equation reduces to a first-order transfer equation.
Integrable cosmological models from higher dimensional Einstein equations
Sano, Masakazu; Suzuki, Hisao
2007-09-15
We consider the cosmological models for the higher dimensional space-time which includes the curvatures of our space as well as the curvatures of the internal space. We find that the condition for the integrability of the cosmological equations is that the total space-time dimensions are D=10 or D=11 which is exactly the conditions for superstrings or M theory. We obtain analytic solutions with generic initial conditions in the four-dimensional Einstein frame and study the accelerating universe when both our space and the internal space have negative curvatures.
High spacecraft potentials on ISEE-1 in sunlight
NASA Technical Reports Server (NTRS)
Whipple, E. C., Jr.; Olsen, R. C.
1987-01-01
Data from two electric field experiments and from the plasma composition experiment on ISEE-1 show that the spacecraft charged to close to -70 V in sunlight at about 0700 UT on March 17, 1978. Data from the electron spectrometer experiment show that there was a potential barrier of some -10 to -20 V about the spacecraft during this event. The potential barrier was effective in turning back emitted photoelectrons to the spacecraft. Potential barriers can be formed by differential charging on the spacecraft or by the presence of space charge. The stringent electrostatic cleanliness specifications imposed on ISEE made the presence of differential charging seem unlikely, if these precautions were effective. Modeling of the event to determine if the barrier was produced by the presence of space charge suggested that this could not explain the observed barrier. The angular shape of the distribution could be successfully modeled as a product of differential charging on the solar arrays. This implies that the conductive coating was not completely effective in preventing differential charging, and that differential charging did occur.
Approaches to verification of two-dimensional water quality models
Butkus, S.R. . Water Quality Dept.)
1990-11-01
The verification of a water quality model is the one procedure most needed by decision making evaluating a model predictions, but is often not adequate or done at all. The results of a properly conducted verification provide the decision makers with an estimate of the uncertainty associated with model predictions. Several statistical tests are available for quantifying of the performance of a model. Six methods of verification were evaluated using an application of the BETTER two-dimensional water quality model for Chickamauga reservoir. Model predictions for ten state variables were compared to observed conditions from 1989. Spatial distributions of the verification measures showed the model predictions were generally adequate, except at a few specific locations in the reservoir. The most useful statistics were the mean standard error of the residuals. Quantifiable measures of model performance should be calculated during calibration and verification of future applications of the BETTER model. 25 refs., 5 figs., 7 tabs.
A refined one-dimensional rotordynamics model with three-dimensional capabilities
NASA Astrophysics Data System (ADS)
Carrera, E.; Filippi, M.
2016-03-01
This paper evaluates the vibration characteristics of various rotating structures. The present methodology exploits the one-dimensional Carrera Unified Formulation (1D CUF), which enables one to go beyond the kinematic assumptions of classical beam theories. According to the component-wise (CW) approach, Lagrange-like polynomial expansions (LE) are here adopted to develop the refined displacement theories. The LE elements make it possible to model each structural component of the rotor with an arbitrary degree of accuracy using either different displacement theories or localized mesh refinements. Hamilton's Principle is used to derive the governing equations, which are solved by the Finite Element Method. The CUF one-dimensional theory includes all the effects due to rotation, namely the Coriolis term, spin softening and geometrical stiffening. The numerical simulations have been performed considering a thin ring, discs and bladed-deformable shafts. The effects of the number and the position of the blades on the dynamic stability of the rotor have been evaluated. The results have been compared, when possible, with the 2D and 3D solutions that are available in the literature. CUF models appear very practical to investigate the dynamics of complex rotating structures since they provide 2D and quasi-3D results, while preserving the computational effectiveness of one-dimensional solutions.
Three-dimensional "Mercedes-Benz" model for water.
Dias, Cristiano L; Ala-Nissila, Tapio; Grant, Martin; Karttunen, Mikko
2009-08-01
In this paper we introduce a three-dimensional version of the Mercedes-Benz model to describe water molecules. In this model van der Waals interactions and hydrogen bonds are given explicitly through a Lennard-Jones potential and a Gaussian orientation-dependent terms, respectively. At low temperature the model freezes forming Ice-I and it reproduces the main peaks of the experimental radial distribution function of water. In addition to these structural properties, the model also captures the thermodynamical anomalies of water: The anomalous density profile, the negative thermal expansivity, the large heat capacity, and the minimum in the isothermal compressibility. PMID:19673572
Three-dimensional ``Mercedes-Benz'' model for water
NASA Astrophysics Data System (ADS)
Dias, Cristiano L.; Ala-Nissila, Tapio; Grant, Martin; Karttunen, Mikko
2009-08-01
In this paper we introduce a three-dimensional version of the Mercedes-Benz model to describe water molecules. In this model van der Waals interactions and hydrogen bonds are given explicitly through a Lennard-Jones potential and a Gaussian orientation-dependent terms, respectively. At low temperature the model freezes forming Ice-I and it reproduces the main peaks of the experimental radial distribution function of water. In addition to these structural properties, the model also captures the thermodynamical anomalies of water: The anomalous density profile, the negative thermal expansivity, the large heat capacity, and the minimum in the isothermal compressibility.
A one-dimensional basic oscillator model of the vircator
NASA Astrophysics Data System (ADS)
Biswas, Debabrata
2009-06-01
A one-dimensional model of the virtual cathode oscillator (vircator) is proposed keeping only the essential physical processes. The basic model consists of a radiating charge in an oscillating electric field. Using parameters from (realistic) particle-in-cell simulations such as the charge Q and amplitude E1 of the oscillating electric field, the model correctly predicts the amplitude of virtual cathode oscillation and the power radiated. The basic model is then extended to incorporate beam-cavity interaction and the resonance effect.
SOLVING THE TWO-DIMENSIONAL DIFFUSION FLOW MODEL.
Hromadka, T.V., II; Lai, Chintu
1985-01-01
A simplification of the two-dimensional (2-D) continuity and momentum equations is the diffusion equation. To investigate its capability, the numerical model using the diffusion approach is applied to a hypothetical failure problem of a regional water reservoir. The model is based on an explicit, integrated finite-difference scheme, and the floodplain is simulated by a popular home computer which supports 64K FORTRAN. Though simple, the 2-D model can simulate some interesting flooding effects that a 1-D full dynamic model cannot.
Four-Dimensional Global Reference-Atmosphere Model
NASA Technical Reports Server (NTRS)
Johnson, Dale; Blocker, Rhonda S.
1988-01-01
Four-Dimensional Global Reference Atmosphere Model (GRAM) computer program developed from empirical atmospheric model generating values for pressure, density, temperature, and winds, from ground to orbital altitudes. Is amalgamation of two empirical atmospheric models for low and high atmosphere with newly-developed latitude-and longitude-dependent model for middle atmosphere. UNIVAC version written in UNIVAC FORTRAN. DEC VAX version of GRAM written in FORTRAN 77. Applications include simulation of reentry trajectories of external tanks, studies of global circulation and diffusion and generation of plots or data for comparison.
Two-dimensional Core-collapse Supernova Models with Multi-dimensional Transport
NASA Astrophysics Data System (ADS)
Dolence, Joshua C.; Burrows, Adam; Zhang, Weiqun
2015-02-01
We present new two-dimensional (2D) axisymmetric neutrino radiation/hydrodynamic models of core-collapse supernova (CCSN) cores. We use the CASTRO code, which incorporates truly multi-dimensional, multi-group, flux-limited diffusion (MGFLD) neutrino transport, including all relevant {O}(v/c) terms. Our main motivation for carrying out this study is to compare with recent 2D models produced by other groups who have obtained explosions for some progenitor stars and with recent 2D VULCAN results that did not incorporate {O}(v/c) terms. We follow the evolution of 12, 15, 20, and 25 solar-mass progenitors to approximately 600 ms after bounce and do not obtain an explosion in any of these models. Though the reason for the qualitative disagreement among the groups engaged in CCSN modeling remains unclear, we speculate that the simplifying "ray-by-ray" approach employed by all other groups may be compromising their results. We show that "ray-by-ray" calculations greatly exaggerate the angular and temporal variations of the neutrino fluxes, which we argue are better captured by our multi-dimensional MGFLD approach. On the other hand, our 2D models also make approximations, making it difficult to draw definitive conclusions concerning the root of the differences between groups. We discuss some of the diagnostics often employed in the analyses of CCSN simulations and highlight the intimate relationship between the various explosion conditions that have been proposed. Finally, we explore the ingredients that may be missing in current calculations that may be important in reproducing the properties of the average CCSNe, should the delayed neutrino-heating mechanism be the correct mechanism of explosion.
TWO-DIMENSIONAL CORE-COLLAPSE SUPERNOVA MODELS WITH MULTI-DIMENSIONAL TRANSPORT
Dolence, Joshua C.; Burrows, Adam; Zhang, Weiqun E-mail: burrows@astro.princeton.edu
2015-02-10
We present new two-dimensional (2D) axisymmetric neutrino radiation/hydrodynamic models of core-collapse supernova (CCSN) cores. We use the CASTRO code, which incorporates truly multi-dimensional, multi-group, flux-limited diffusion (MGFLD) neutrino transport, including all relevant O(v/c) terms. Our main motivation for carrying out this study is to compare with recent 2D models produced by other groups who have obtained explosions for some progenitor stars and with recent 2D VULCAN results that did not incorporate O(v/c) terms. We follow the evolution of 12, 15, 20, and 25 solar-mass progenitors to approximately 600 ms after bounce and do not obtain an explosion in any of these models. Though the reason for the qualitative disagreement among the groups engaged in CCSN modeling remains unclear, we speculate that the simplifying ''ray-by-ray'' approach employed by all other groups may be compromising their results. We show that ''ray-by-ray'' calculations greatly exaggerate the angular and temporal variations of the neutrino fluxes, which we argue are better captured by our multi-dimensional MGFLD approach. On the other hand, our 2D models also make approximations, making it difficult to draw definitive conclusions concerning the root of the differences between groups. We discuss some of the diagnostics often employed in the analyses of CCSN simulations and highlight the intimate relationship between the various explosion conditions that have been proposed. Finally, we explore the ingredients that may be missing in current calculations that may be important in reproducing the properties of the average CCSNe, should the delayed neutrino-heating mechanism be the correct mechanism of explosion.
Equation of State of the Two-Dimensional Hubbard Model.
Cocchi, Eugenio; Miller, Luke A; Drewes, Jan H; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael
2016-04-29
The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0≲U/t≲20 and temperatures, down to k_{B}T/t=0.63(2) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches. PMID:27176527
Equation of State of the Two-Dimensional Hubbard Model
NASA Astrophysics Data System (ADS)
Cocchi, Eugenio; Miller, Luke A.; Drewes, Jan H.; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael
2016-04-01
The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0 ≲U /t ≲20 and temperatures, down to kBT /t =0.63 (2 ) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches.
Three Dimensional Thermal Abuse Reaction Model for Lithium Ion Batteries
2006-06-29
Three dimensional computer models for simulating thermal runaway of lithium ion battery was developed. The three-dimensional model captures the shapes and dimensions of cell components and the spatial distributions of materials and temperatures, so we could consider the geometrical features, which are critical especially in large cells. An array of possible exothermic reactions, such as solid-electrolyte-interface (SEI) layer decomposition, negative active/electrolyte reaction, and positive active/electrolyte reaction, were considered and formulated to fit experimental data frommore » accelerating rate calorimetry and differential scanning calorimetry. User subroutine code was written to implement NREL developed approach and to utilize a commercially available solver. The model is proposed to use for simulation a variety of lithium-ion battery safety events including thermal heating and short circuit.« less
An interactive three-dimensional nose model for rhinosurgery.
Heppt, Werner Johannes; Godbersen, Heinrich; Hildebrandt, Thomas
2013-04-01
The motivation behind the development of a new interactive three-dimensional (3D) model of the cartilaginous and bony framework of the nose originated from the significant demand for sophisticated patient communication and for accurate documentation of the surgical steps in rhinoplasty. Basically, the model consists of three features--the viewer function, the freehand function, and default applications--enabling the surgeon to replicate fundamental compilations of findings and to graphically document operative measures easily. The user is able to save all graphics in two-dimensional format and allocate them to patient files. Because the application was designed to be sufficiently universal without being too complex, the 3D model provides a well-balanced mix between freehand and default functions, representing the consistent development of currently available tools. PMID:23564244
Three Dimensional Thermal Abuse Reaction Model for Lithium Ion Batteries
and Ahmad Pesaran, Gi-Heon Kim
2006-06-29
Three dimensional computer models for simulating thermal runaway of lithium ion battery was developed. The three-dimensional model captures the shapes and dimensions of cell components and the spatial distributions of materials and temperatures, so we could consider the geometrical features, which are critical especially in large cells. An array of possible exothermic reactions, such as solid-electrolyte-interface (SEI) layer decomposition, negative active/electrolyte reaction, and positive active/electrolyte reaction, were considered and formulated to fit experimental data from accelerating rate calorimetry and differential scanning calorimetry. User subroutine code was written to implement NREL developed approach and to utilize a commercially available solver. The model is proposed to use for simulation a variety of lithium-ion battery safety events including thermal heating and short circuit.
A three-dimensional model of Tangential YORP
Golubov, O.; Scheeres, D. J.; Krugly, Yu. N.
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 via 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.
Statistical mechanics of shell models for two-dimensional turbulence
NASA Astrophysics Data System (ADS)
Aurell, E.; Boffetta, G.; Crisanti, A.; Frick, P.; Paladin, G.; Vulpiani, A.
1994-12-01
We study shell models that conserve the analogs of energy and enstrophy and hence are designed to mimic fluid turbulence in two-dimensions (2D). The main result is that the observed state is well described as a formal statistical equilibrium, closely analogous to the approach to two-dimensional ideal hydrodynamics of Onsager [Nuovo Cimento Suppl. 6, 279 (1949)], Hopf [J. Rat. Mech. Anal. 1, 87 (1952)], and Lee [Q. Appl. Math. 10, 69 (1952)]. In the presence of forcing and dissipation we observe a forward flux of enstrophy and a backward flux of energy. These fluxes can be understood as mean diffusive drifts from a source to two sinks in a system which is close to local equilibrium with Lagrange multipliers (``shell temperatures'') changing slowly with scale. This is clear evidence that the simplest shell models are not adequate to reproduce the main features of two-dimensional turbulence. The dimensional predictions on the power spectra from a supposed forward cascade of enstrophy and from one branch of the formal statistical equilibrium coincide in these shell models in contrast to the corresponding predictions for the Navier-Stokes and Euler equations in 2D. This coincidence has previously led to the mistaken conclusion that shell models exhibit a forward cascade of enstrophy. We also study the dynamical properties of the models and the growth of perturbations.
A three-dimensional spin-diffusion model for micromagnetics
Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Hrkac, Gino; Praetorius, Dirk; Suess, Dieter
2015-01-01
We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation. PMID:26442796
A three-dimensional spin-diffusion model for micromagnetics.
Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Hrkac, Gino; Praetorius, Dirk; Suess, Dieter
2015-01-01
We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation. PMID:26442796
A three-dimensional spin-diffusion model for micromagnetics
NASA Astrophysics Data System (ADS)
Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Hrkac, Gino; Praetorius, Dirk; Suess, Dieter
2015-10-01
We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation.
Two dimensional hydrodynamic modeling of a high latitude braided river
NASA Astrophysics Data System (ADS)
Humphries, E.; Pavelsky, T.; Bates, P. D.
2014-12-01
Rivers are a fundamental resource to physical, ecologic and human systems, yet quantification of river flow in high-latitude environments remains limited due to the prevalence of complex morphologies, remote locations and sparse in situ monitoring equipment. Advances in hydrodynamic modeling and remote sensing technology allow us to address questions such as: How well can two-dimensional models simulate a flood wave in a highly 3-dimensional braided river environment, and how does the structure of such a flood wave differ from flow down a similar-sized single-channel river? Here, we use the raster-based hydrodynamic model LISFLOOD-FP to simulate flood waves, discharge, water surface height, and velocity measurements over a ~70 km reach of the Tanana River in Alaska. In order to use LISFLOOD-FP a digital elevation model (DEM) fused with detailed bathymetric data is required. During summer 2013, we surveyed 220,000 bathymetric points along the study reach using an echo sounder system connected to a high-precision GPS unit. The measurements are interpolated to a smooth bathymetric surface, using Topo to Raster interpolation, and combined with an existing five meter DEM (Alaska IfSAR) to create a seamless river terrain model. Flood waves are simulated using varying complexities in model solvers, then compared to gauge records and water logger data to assess major sources of model uncertainty. Velocity and flow direction maps are also assessed and quantified for detailed analysis of braided channel flow. The most accurate model output occurs with using the full two-dimensional model structure, and major inaccuracies appear to be related to DEM quality and roughness values. Future work will intercompare model outputs with extensive ground measurements and new data from AirSWOT, an airborne analog for the Surface Water and Ocean Topography (SWOT) mission, which aims to provide high-resolution measurements of terrestrial and ocean water surface elevations globally.
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
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.
NASA Astrophysics Data System (ADS)
Coudert, L. H.
2015-01-01
Torsional control is studied theoretically using a four-dimensional (4D) model introduced recently [Phys. Rev. Lett. 107, 113004 (2011), 10.1103/PhysRevLett.107.113004 and Phys. Rev. A 87, 043403 (2013), 10.1103/PhysRevA.87.043403] for calculating energy levels and eigenfunctions of nonrigid biphenyl-like molecules undergoing internal rotation and subject to a strong electric field. The time-dependent Schrödinger equation is solved to determine the behavior of the molecule when submitted to a short laser pulse. Torsional alignment is investigated for four limiting hindering potentials and for several peak laser intensities. The results obtained with the 4D model are compared to those from already available 2D and 1D models. Similar results are found with the 4D and 2D model and are consistent with the molecule interacting the most with the electric field for the hindering potential displaying four minima with D2 d symmetry staggered equilibrium configurations. Molecular axis alignment is also investigated and it is found that the one arising with the 4D model starts deviating substantially from the one arising with a rigid rotator for a value of the peak laser intensity of 3 ×1013 W/cm 2.
Anisotropy of stress correlation in two-dimensional liquids and a pseudospin model
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
Anisotropy of stress correlation in two-dimensional liquids and a pseudospin model
NASA Astrophysics Data System (ADS)
Wu, Bin; Iwashita, Takuya; Egami, Takeshi
2015-11-01
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. In this paper, 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. The connection between SRPDFs and stress correlation function is explained through an approximation in which the shear stress is replaced by a pseudospin. We further assess the possibility of interpreting the long-range stress correlation as a consequence of short-range Ising-like pseudospin interactions.
Anisotropy of stress correlation in two-dimensional liquids and a pseudospin model.
Wu, Bin; Iwashita, Takuya; Egami, Takeshi
2015-11-01
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. In this paper, 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. The connection between SRPDFs and stress correlation function is explained through an approximation in which the shear stress is replaced by a pseudospin. We further assess the possibility of interpreting the long-range stress correlation as a consequence of short-range Ising-like pseudospin interactions. PMID:26651691