Related papers: On Critical Temperature and Finite Size Scaling of…
We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to L=40 using the Janus dedicated computer. Our…
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 investigated the Ising model on a square lattice with ferro and antiferromagnetic interactions modulated by the quasiperiodic Octonacci sequence in both directions of the lattice. We have applied the Replica Exchange Monte Carlo…
We study the block spin transformation for the 2D Ising model at the critical temperature $T_c$. We consider the model with the constraint that the total spin in each block is zero. An old argument by Cassandro and Gallavotti allows to show…
We have studied the three-dimensional Ising spin glass with a $\pm J$ distribution by Monte Carlo simulations. Using larger sizes and much better statistics than in earlier work, a finite size scaling analysis shows quite strong evidence…
While the 3d Ising model has defied analytic solution, various numerical methods like Monte Carlo, MCRG and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff…
We study the Ising model on $\mathbb{Z}^{2}$ and show, via numerical simulation, that allowing interactions between spins separated by distances $1$ and $m$ (two ranges), the critical temperature, $ T_c (m) $, converges monotonically to the…
Extensive Monte Carlo study of two-dimensional Ising model is done to investigate the statistical behavior of spin clusters and interfaces as a function of temperature, $T$. We use a \emph{tie-breaking} rule to define interfaces of spin…
We compare numerical estimates from different sources for the ordering temperature $T_g$ and the critical exponents of the Ising spin glass in dimension three with binomial ($\pm J$) interactions. Corrections to finite size scaling turn out…
The edge-cubic spin model on square lattice is studied via Monte Carlo simulation with cluster algorithm. By cooling the system, we found two successive symmetry breakings, i.e., the breakdown of $O_h$ into the group of $C_{3h}$ which then…
The critical behavior of the Ising model with non-conserved dynamics and an external shear profile is analyzed by studying its dynamical evolution in the short time regime. Starting from high temperature disordered configurations (FDC), the…
A periodic Ising model is one endowed with interactions that are invariant under translations of members of a full-rank sublattice $\mathfrak{L}$ of $\mathbb{Z}^2$. We give an exact, quantitative description of the critical temperature,…
We have simulated, using parallel tempering, the three dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice (L=20) has been studied using a dedicated computer (the SUE machine). We have…
We have performed Monte Carlo studies of the 3D $XY$ model with random uniaxial anisotropy, which is a model for randomly pinned spin-density waves. We study $L \times L \times L$ simple cubic lattices, using $L$ values in the range 16 to…
We study the ordering of the spin and the chirality in the fully frustrated XY model on a square lattice by extensive Monte Carlo simulations. Our results indicate unambiguously that the spin and the chirality exhibit separate phase…
We investigate deep learning autoencoders for the unsupervised recognition of phase transitions in physical systems formulated on a lattice. We focus our investigation on the 2-dimensional ferromagnetic Ising model and then test the…
We investigate the complex-temperature singularities of the susceptibility of the 2D Ising model on a square lattice. From an analysis of low-temperature series expansions, we find evidence that as one approaches the point $u=u_s=-1$ (where…
We simulate the spin-1/2 Ising model and the Blume-Capel model at various values of the parameter D on the simple cubic lattice. We perform a finite size scaling study of lattices of a linear size up to L=360 to obtain accurate estimates…
We derive low-temperature series (in the variable $u = \exp[-\beta J/S^2]$) for the spontaneous magnetisation, susceptibility and specific heat of the spin-$S$ Ising model on the square lattice for $S=\frac32$, 2, $\frac52$, and 3. We…
A new method for locating analytically critical temperatures is discussed. It is exact for selfdual systems. When applied the two coupled layers of Ising spins it deviates from our preliminary Monte Carlo estimates by 1.5 standard…