A New Measurement of Dynamic Critical exponent of Wolff Algorithm by Dynamic Finite Size Scaling

TL;DR

This paper measures the dynamic critical exponent of the Wolff algorithm for 2D, 3D, and 4D Ising models using dynamic finite size scaling, confirming universality and finding very small z values.

Contribution

It introduces a new measurement of the dynamic critical exponent for the Wolff algorithm across multiple dimensions using dynamic finite size scaling.

Findings

Dynamic scaling is independent of the algorithm.

Universality of dynamic scaling is established.

Very small z values are observed for all three dimensions.

Abstract

In this work we have calculated the dynamic critical exponent $z$ for 2-, 3- and 4-dimensional Ising models using the Wolff's algorithm through dynamic finite size scaling. We have studied time evolution of the average cluster size, the magnetization and higher moments of the magnetization. It is observed that dynamic scaling is independent of the algorithm. In this sense, universality is established for a wide range of algorithms with their own dynamic critical exponents. For scaling, we have used the literature values of critical exponents to observe the dynamic finite size scaling and to obtain the value of $z$. From the simulation data a very good scaling is observed leading to vanishingly small $z$ values for all three dimensions.