Finite-size Scaling of Correlation Ratio and Generalized Scheme for the Probability-Changing Cluster Algorithm

TL;DR

This paper demonstrates that the correlation ratio is an effective finite-size scaling estimator for critical points, especially in Kosterlitz-Thouless transitions, and introduces a generalized probability-changing cluster algorithm for efficient analysis.

Contribution

The authors propose a generalized scheme for the probability-changing cluster algorithm based on the correlation ratio's FSS properties, improving efficiency in identifying critical points.

Findings

Correlation ratio accurately estimates critical points in FSS analysis.

The generalized algorithm effectively determines the KT transition temperature.

Reduced computational effort in analyzing the 2D quantum XY model.

Abstract

We study the finite-size scaling (FSS) property of the correlation ratio, the ratio of the correlation functions with different distances. It is shown that the correlation ratio is a good estimator to determine the critical point of the second-order transition using the FSS analysis. The correlation ratio is especially useful for the analysis of the Kosterlitz-Thouless (KT) transition. We also present a generalized scheme of the probability-changing cluster algorithm, which has been recently developed by the present authors, based on the FSS property of the correlation ratio. We investigate the two-dimensional quantum XY model of spin 1/2 with this generalized scheme, obtaining the precise estimate of the KT transition temperature with less numerical effort.