Correlation-function approach to the critical properties of the three-dimensional XY model

Abstract

The critical properties of the three-dimensional XY model are investigated through measurements of the two-point correlation functions via a worm-algorithm Monte Carlo calculation, which automatically crunches the correlation functions while tracing worms, in large systems. This method has the advantage of directly measuring the order parameter, as well as the correlation length, the susceptibility, and their associated critical exponents. From the finite-size scaling behavior, we find 2β/ν = 1.033(5) and γ/ν = 1.967(5), confirming the hyperscaling relations.