Topic
Ising model
About: Ising model is a research topic. Over the lifetime, 25508 publications have been published within this topic receiving 555000 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, a Monte Carlo simulation of lattice models is used to determine the Casimir forces acting on the confining surfaces of soft media for the Ising and the XY universality classes.
Abstract: The confinement of critical fluctuations in soft media induces critical Casimir forces acting on the confining surfaces. The temperature and geometry dependences of such forces are characterized by universal scaling functions. A novel approach is presented to determine them for films via Monte Carlo simulations of lattice models. The method is based on an integration scheme of free energy differences. Our results for the Ising and the XY universality class agree well with corresponding experimental results for wetting layers of classical binary liquid mixtures and of 4He, respectively.
128 citations
15 Jun 1997
TL;DR: In this article, the effects of magnetic frustation in the stacked triangular lattice were reviewed and the authors described the confrontation of theory and experiment for a number of systems with differing magnetic Hamiltonians.
Abstract: In this article we review the effects of magnetic frustation in the stacked triangular lattice. Frustration increases the degeneracy of the ground state, giving rise to different physics. In particular it leads to unique phase diagrams with multicritical points and novel critical phenomena. We describe the confrontation of theory and experiment for a number of systems with differing magnetic Hamiltonians; Heisenberg, Heisenberg with easy-axis anisotropy, Heisenberg with easy-plane anisotropy, Ising and singlet ground state. Interestingly each leads to different magnetic properties and phase diagrams. We also describe the effects of ferromagnetic, rather than antiferromagnetic, stacking and of small distortions of the triangular lattice.
128 citations
TL;DR: This work has investigated the critical behavior of the simple cubic Ising Model, using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic.
Abstract: While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from ${16}^{3}$ to ${1024}^{3}$. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature ${K}_{c}=0.221\phantom{\rule{0.16em}{0ex}}654\phantom{\rule{0.16em}{0ex}}626(5)$ and the critical exponent of the correlation length $\ensuremath{
u}=0.629\phantom{\rule{0.16em}{0ex}}912(86)$ with precision that exceeds all previous Monte Carlo estimates.
127 citations
TL;DR: In this article, it was shown that the metastable states which are relevant for the out-of-equilibrium dynamics of such systems are always in a FRSB phase.
Abstract: The low-temperature phase of discontinuous mean-field spin glasses is generally described by a one-step replica symmetry breaking (1RSB) ansatz. The Gardner transition, i.e. a very-low-temperature phase transition to a full replica symmetry breaking (FRSB) phase, is often regarded as an inessential, and somehow exotic phenomenon. In this paper we show that the metastable states which are relevant for the out-of-equilibrium dynamics of such systems are always in a FRSB phase. The only exceptions are (to the best of our knowledge) the p-spin spherical model and the random energy model (REM). We also discuss the consequences of our results for aging dynamics and for local search algorithms in hard combinatorial problems.
127 citations
TL;DR: In this paper, it was shown that the two-dimensional free fermion model is equivalent to a checkboard Ising model, which is a special case of the general Z -invariant Ising Model.
Abstract: It is shown that the two-dimensional free fermion model is equivalent to a checkerboard Ising model, which is a special case of the general ‘ Z -invariant’ Ising model Expressions are given for the partition function and local correlations in terms of those of the regular square lattice Ising model Corresponding results are given for the self-dual Potts model, and the application of the methods to the three-dimensional Zamolodchikov model is discussed The paper ends with a discussion of the critical and disorder surfaces of the checkerboard Potts model
127 citations