A Study of Dynamic Finite Size Scaling Behavior of the Scaling Functions-Calculation of Dynamic Critical Index of Wolff Algorithm

TL;DR

This paper investigates the dynamic finite size scaling behavior of scaling functions and uses this to accurately calculate the dynamic critical exponent of Wolff's algorithm for Ising models in multiple dimensions, showing improved efficiency.

Contribution

It demonstrates that scaling functions follow dynamic finite size scaling rules and uses this to determine the dynamic critical exponent of Wolff's algorithm across different dimensions.

Findings

Scaling functions obey dynamic finite size scaling rules.

Calculated dynamic critical exponents for 2D, 3D, and 4D Ising models.

Wolff algorithm shows reduced critical slowing down, especially in 3D.

Abstract

In this work we have studied the dynamic scaling behavior of two scaling functions and we have shown that scaling functions obey the dynamic finite size scaling rules. Dynamic finite size scaling of scaling functions opens possibilities for a wide range of applications. As an application we have calculated the dynamic critical exponent ($z$) of Wolff's cluster algorithm for 2-, 3- and 4-dimensional Ising models. Configurations with vanishing initial magnetization are chosen in order to avoid complications due to initial magnetization. The observed dynamic finite size scaling behavior during early stages of the Monte Carlo simulation yields $z$ for Wolff's cluster algorithm for 2-, 3- and 4-dimensional Ising models with vanishing values which are consistent with the values obtained from the autocorrelations. Especially, the vanishing dynamic critical exponent we obtained for $d=3$ implies that the Wolff algorithm is more efficient in eliminating critical slowing down in Monte Carlo simulations than previously reported.