Probability-Changing Cluster Algorithm: Study of Three-Dimensional Ising Model and Percolation Problem

TL;DR

This paper introduces the probability-changing cluster (PCC) algorithm, an innovative Monte Carlo method that automatically tunes the critical point, and applies it to study the 3D Ising model and percolation, achieving consistent results efficiently.

Contribution

The paper presents a new Monte Carlo algorithm, the PCC, that automatically adjusts the critical point, simplifying critical phenomena simulations and analysis.

Findings

Accurate estimates of critical points and exponents for 3D Ising and percolation.

Demonstration of the PCC algorithm's efficiency and consistency with previous results.

Discussion of potential applications of the PCC algorithm.

Abstract

We present a detailed description of the idea and procedure for the newly proposed Monte Carlo algorithm of tuning the critical point automatically, which is called the probability-changing cluster (PCC) algorithm [Y. Tomita and Y. Okabe, Phys. Rev. Lett. {\bf 86} (2001) 572]. Using the PCC algorithm, we investigate the three-dimensional Ising model and the bond percolation problem. We employ a refined finite-size scaling analysis to make estimates of critical point and exponents. With much less efforts, we obtain the results which are consistent with the previous calculations. We argue several directions for the application of the PCC algorithm.