Ising model

About: Ising model is a research topic. Over the lifetime, 25508 publications have been published within this topic receiving 555000 citations.

Monte Carlo investigation of a kinetic Ising model of the glass transition

Abstract: A detailed Monte Carlo study of the equilibrium and dynamical properties of the two‐spin facilitated kinetic Ising model proposed by Fredrickson and Andersen (FA) is presented. The model Hamiltonian is that of a spin‐1/2 Ising model in an external magnetic field and, in the present study, contains no interactions between spins. The kinetic properties of the model are described by a master equation with single‐spin‐flip dynamics and highly cooperative flip rates. In particular, the rate at which a spin flips is chosen to be zero unless at least two of its neighbors are spin up. Monte Carlo simulations of the model on a square lattice demonstrate that although there is no evidence for a kinetic singularity (as predicted by FA), the model has dynamical properties much like those of viscous liquids. We find non‐Arrhenius temperature dependence of the average relaxation time and highly nonexponential decay of various relaxation functions. The expression derived by Adam and Gibbs is found to describe the relationship between the average relaxation time and the entropy of the spin model. It is shown that the equilibrium time correlation functions can be accurately fit to the Kohlrausch–Williams–Watts (KWW) expression. The exponent in the KWW function is found to decrease as the temperature is lowered. Studies of multiple‐spin correlation functions demonstrate how spatial correlations develop in the model as it is perturbed from equilibrium and how these relax as the system equilibrates.

Flexoelectricity and Ferroelectric Domain Wall Structures: Phase-Field Modeling and DFT Calculations

Abstract: We show that flexoelectric effect is responsible for the non-Ising character of a 180\ifmmode^\circ\else\textdegree\fi{} ferroelectric domain wall. The wall, long considered being of Ising type, contains both Bloch- and N\'eel-type polarization components. Using the example of classic ferroelectric ${\mathrm{BaTiO}}_{3}$, and by incorporating the flexoelectric effect into a phase-field model, it is demonstrated that the flexoelectric effect arising from stress inhomogeneity around the domain wall leads to the additional Bloch and N\'eel polarization components. The magnitudes of these additional components are two or three magnitudes smaller than the Ising component, and they are determined by the competing depolarization and flexoelectric fields. Our results from phase-field model are consistent with the atomistic scale calculations. The results prove the critical role of flexoelectricity in defining the internal structure of ferroelectric domain walls.

Chain length dependence of the polymer-solvent critical point parameters

Abstract: We report grand canonical Monte Carlo simulations of the critical point properties of homopolymers within the bond fluctuation model. By employing configurational bias Monte Carlo methods, chain lengths of up to N=60 monomers could be studied. For each chain length investigated, the critical point parameters were determined by matching the ordering operator distribution function to its universal fixed‐point Ising form. Histogram reweighting methods were employed to increase the efficiency of this procedure. The results indicate that the scaling of the critical temperature with chain length is relatively well described by Flory theory, i.e., Θ−Tc∼N−0.5. The critical volume fraction, on the other hand, was found to scale like φc∼N−0.37, in clear disagreement with the Flory theory prediction φc∼N−0.5, but in good agreement with experiment. Measurements of the chain length dependence of the end‐to‐end distance indicate that the chains are not collapsed at the critical point.

Reexamining classical and quantum models for the D-Wave One processor

Abstract: We revisit the evidence for quantum annealing in the D-Wave One device (DW1) based on the study of random Ising instances. Using the probability distributions of finding the ground states of such instances, previous work found agreement with both simulated quantum annealing (SQA) and a classical rotor model. Thus the DW1 ground state success probabilities are consistent with both models, and a different measure is needed to distinguish the data and the models. Here we consider measures that account for ground state degeneracy and the distributions of excited states, and present evidence that for these new measures neither SQA nor the classical rotor model correlate perfectly with the DW1 experiments. We thus provide evidence that SQA and the classical rotor model, both of which are classically efficient algorithms, do not satisfactorily explain all the DW1 data. A complete model for the DW1 remains an open problem. Using the same criteria we find that, on the other hand, SQA and the classical rotor model correlate closely with each other. To explain this we show that the rotor model can be derived as the semiclassical limit of the spin-coherent states path integral. We also find differences in which set of ground states is found by each method, though this feature is sensitive to calibration errors of the DW1 device and to simulation parameters.