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

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).