Large-scale Monte Carlo simulation of two-dimensional classical XY model using multiple GPUs

TL;DR

This paper presents large-scale GPU-accelerated Monte Carlo simulations of the 2D XY model to accurately determine the Kosterlitz-Thouless transition temperature and logarithmic correction exponent.

Contribution

It introduces a GPU-based implementation of the Swendsen-Wang algorithm for large systems and accurately locates the KT transition and correction exponent.

Findings

KT transition temperature 119.96(6)

Logarithmic correction exponent 1/8

Successful simulation of systems up to size 65536

Abstract

We study the two-dimensional classical XY model by the large-scale Monte Carlo simulation of the Swendsen-Wang multi-cluster algorithm using multiple GPUs on the open science supercomputer TSUBAME 2.0. Simulating systems up to the linear system size L=65536, we investigate the Kosterlitz-Thouless (KT) transition. Using the generalized version of the probability-changing cluster algorithm based on the helicity modulus, we locate the KT transition temperature in a self-adapted way. The obtained inverse KT temperature \beta_{KT} is 1.11996(6). We estimate the exponent to specify the multiplicative logarithmic correction, -2r, and precisely reproduce the theoretical prediction -2r=1/8.