Large-Scale Monte Carlo Simulation of Two-Dimensional Classical XY Model Using Multiple GPUs

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 β_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.