The influence of the Wolff's cluster structure on the determination of the critical dynamic exponent

TL;DR

This paper investigates how the Wolff's cluster structure and spatial correlations influence the critical dynamic exponent in the Ising model, revealing that stronger correlations reduce autocorrelation time without altering the exponent.

Contribution

It provides a detailed analysis of the Wolff's cluster structure variations with spatial correlation and estimates the critical dynamic exponent based on fractal dimensions.

Findings

Stronger correlations decrease autocorrelation time.

The critical dynamic exponent remains unaffected by correlation strength.

Fractal dimensions vary with magnetic atom concentration and correlation.

Abstract

Recently we reported some interesting features of the Wolff's algorithm behavior when applied to the site-bond-correlated Ising model.Our main results were that a stronger correlation diminishes the autocorrelation time but it does not change or affectthe critical dynamic exponent.In this paper, we analyse the Wolff's cluster structure and how it varies with the spatial correlation. The fractal dimensions are determined for several values of the magnetic atoms concentration and spacial correlation, giving an estimative of the critical dynamic exponent.