Two-size Probability-Changing Cluster Algorithm

TL;DR

This paper introduces a self-adaptive Monte Carlo method that automatically finds critical temperatures for various phase transitions by comparing two systems of different sizes, improving precision and versatility.

Contribution

The novel approach uses a negative feedback mechanism to accurately determine critical points across different types of phase transitions without prior knowledge.

Findings

Effective in locating critical temperatures for second-order phase transitions

Applicable to first-order and Berezinskii-Kosterlitz-Thouless transitions

Provides precise thermal averages near critical points

Abstract

We propose a self-adapted Monte Carlo approach to automatically determine the critical temperature by simulating two systems with different sizes at the same temperature. The temperature is increased or decreased by checking the short-time average of the correlation ratios of the two system sizes. The critical temperature is achieved using the negative feedback mechanism, and the thermal average near the critical temperature can be calculated precisely. The proposed approach is a general method to treat second-order phase transition, first-order phase transition, and Berezinskii-Kosterlitz-Thouless transition on the equal footing.