  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.
