Related papers: High-resolution Monte Carlo study of the order-par…
We study the probability distribution P(M) of the order parameter (average magnetization) M, for the finite-size systems at the critical point. The systems under consideration are the 3-dimensional Ising model on a simple cubic lattice, and…
The probability distribution of the order parameter is exploited in order to obtain the criticality of magnetic systems. Monte Carlo simulations have been employed by using single spin flip Metropolis algorithm aided by finite-size scaling…
The random field Ising model with Gaussian disorder is studied using a new Monte Carlo algorithm. The algorithm combines the advantanges of the replica exchange method and the two-replica cluster method and is much more efficient than the…
We study the three-dimensional Ising model at the critical point in the fixed-magnetization ensemble, by means of the recently developed geometric cluster Monte Carlo algorithm. We define a magnetic-field-like quantity in terms of…
We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin…
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…
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…
Using a cluster-flipping Monte Carlo algorithm combined with a generalization of the histogram reweighting scheme of Ferrenberg and Swendsen, we have studied the equilibrium properties of the thermal random-field Ising model on a cubic…
We discuss several algorithms for sampling from unnormalized probability distributions in statistical physics, but using the language of statistics and machine learning. We provide a self-contained introduction to some key ideas and…
We analyze a controversial question about the universality class of the three-dimensional Ising model with long-range-correlated disorder. Whereas both analytical and numerical studies performed so far support an extended Harris criterion…
Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies…
We present a detailed description of the idea and procedure for the newly proposed Monte Carlo algorithm of tuning the critical point automatically, which is called the probability-changing cluster (PCC) algorithm [Y. Tomita and Y. Okabe,…
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…
The magnetization probability density in d=2 and 3 dimensional Ising models in slab geometry of volume $L_{\parallel}^{d-1} \times L_{\perp}$ is computed through Monte-Carlo simulation at the critical temperature and zero magnetic field.…
We study the order parameter probability distribution at the critical point for the three-dimensional spin-1/2 and spin-1 Ising models on the simple cubic lattice with periodic boundary conditions. The finite size scaling relation for the…
In this paper we propose a Monte Carlo method for generating finite-domain marginals of critical distributions of statistical models in infinite volume. The algorithm corrects the problem of the long-range effects of boundaries associated…
The phase transition of a random mixed-bond Ising ferromagnet on a cubic lattice model is studied both numerically and analytically. In this work, we use the Cluster algorithms of Wolff and Glauber to simulate the dynamics of the system. We…
Based on the connection between the Ising model and a correlated percolation model, we calculate the distribution function for the fraction ($c$) of lattice sites in percolating clusters in subgraphs with $n$ percolating clusters, $f_n(c)$,…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
The Ising model in the presence of a random field is investigated within the mean field approximation based on Landau expansion. The random field is drawn from the trimodal probability distribution $P(h_{i})=p \delta(h_{i}-h_{0}) + q \delta…