Related papers: Numerical Simulations of the Ising Model on the Un…
This paper reviews the work of Wu and Lin on the Union Jack lattice Ising model. This model is of interest as it one of the few to display re-entrant phase transitions. Specifically we re-examine their result for the general anisotropic…
The two-dimensional Ising model is the simplest model of statistical mechanics exhibiting a second order phase transition. While in absence of magnetic field it is known to be solvable on the lattice since Onsager's work of the forties,…
We take the occasion of this article to review one hundred years of the physical and mathematical study of the Ising model. The model, introduced by Lenz in 1920, has been at the cornerstone of many major revolutions in statistical…
We have studied the anisotropic three-dimensional nearest-neighbor Ising model with competitive interactions in an uniform longitudinal magnetic field $H$. The model consists of ferromagnetic interaction $J_{x}(J_{z})$ in the $x(z)$…
We have provided a concise introduction to the Ising model as one of the most important models in statistical mechanics and in studying the phenomenon of phase transition. The required theoretical background and derivation of the…
In this paper we present a simple, yet typical simulation in statistical physics, consisting of large scale Monte Carlo simulations followed by an involved statistical analysis of the results. The purpose is to provide an example…
We conjecture an approximate expression for the free energy in the thermodynamic limit of the classical square lattice Ising model in a uniform (real) magnetic field. The zero-field result is well known due to Onsager for more than eighty…
We studied the phase transitions and magnetic properties of the Ising model on a square lattice by the replica Monte Carlo method and by the method of transfer-matrix, the maximum eigenvalue of which was found by Lanczos method. The…
An asymmetrical 2D Ising model with a zigzag surface, created by diagonally cutting a regular square lattice, has been developed to investigate the thermodynamics and phase transitions on surface by the methodology of recursive lattice,…
Binary magnetic square lattice Ising system with nearest neighbour interactions were simulated using the Monte Carlo technique. Two types of ions were randomly distributed on the lattice sites, one type interacting ferromagnetic and the…
There is no an exact solution to three-dimensional (3D) finite-size Ising model (referred to as the Ising model hereafter for simplicity) and even two-dimensional (2D) Ising model with non-zero external field to our knowledge. Here by using…
A method is proposed for exactly calculating the partition function of a rectangular Ising lattice with the presence of a uniform external field. This approach is based on the method of the transfer matrix developed about seventy years ago…
Lattice models exhibit significant potential in investigating phase transitions, yet they encounter numerous computational challenges. To address these issues, this study introduces a Monte Carlo-based approach that transforms lattice…
We study the statistical Ising model of spins on the infinite lattice using a bootstrap method that combines spin-flip identities with positivity conditions, including reflection positivity and Griffiths inequalities, to derive rigorous…
The Ising model is a simple statistical model for ferromagnetism. There are analytic solutions for low dimensions and very efficient Monte Carlo methods, such as cluster algorithms, for simulating this model in special cases. However most…
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids…
The Monte Carlo with Absorbing Markov Chains (MCAMC) method is introduced. This method is a generalization of the rejection-free method known as the $n$-fold way. The MCAMC algorithm is applied to the study of the very low-temperature…
The critical relaxation from the low-temperature ordered state of the three-dimensional fully frustrated Ising model on a simple cubic lattice has been studied using the short time dynamics method. Particles with the periodic boundary…
When Lenz proposed a simple model for phase transitions in magnetism, he couldn't have imagined that the "Ising model" was to become a jewel in field of equilibrium statistical mechanics. Its role spans the spectrum, from a good pedagogical…
We perform extensive Monte Carlo simulations to investigate the dynamic phase transition properties of the two-dimensional kinetic Ising model on the kagome lattice in the presence of square-wave oscillating magnetic field. Through detailed…