In a strictly short-range XY model made of a plane intersected by parallel planes, true long-range order appears along the intersection lines when the parallel planes enter a Berezinskii-Kosterlitz-Thouless critical phase.
Large-scale Monte Carlo simulation of two-dimensional classical XY model using multiple GPUs
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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.
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Long-Range Order in a Strictly Short-Range Quasi-2D XY Model: When Critical Fluctuations Matter
In a strictly short-range XY model made of a plane intersected by parallel planes, true long-range order appears along the intersection lines when the parallel planes enter a Berezinskii-Kosterlitz-Thouless critical phase.