The Dynamic Exponent of the Two-Dimensional Ising Model and Monte Carlo Computation of the Sub-Dominant Eigenvalue of the Stochastic Matrix

TL;DR

This paper presents a new Monte Carlo algorithm that accurately measures autocorrelation times in 2D Ising models, enabling precise determination of the dynamical critical exponent through finite-size scaling.

Contribution

It introduces a variance-reducing Monte Carlo method for autocorrelation time estimation and applies it to 2D Ising models to determine the dynamical critical exponent.

Findings

Dynamical critical exponent z=2.1665(12) for 2D Ising model

Effective variance reduction in autocorrelation time measurements

Application to systems up to 15x15 spins

Abstract

We introduce a novel variance-reducing Monte Carlo algorithm for accurate determination of autocorrelation times. We apply this method to two-dimensional Ising systems with sizes up to $15 \times 15$, using single-spin flip dynamics, random site selection and transition probabilities according to the heat-bath method. From a finite-size scaling analysis of these autocorrelation times, the dynamical critical exponent $z$ is determined as $z=2.1665$ (12).