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Journal of the Korean Physical Society

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

Min-Chul Cha, Inho Jeon

Published Oct 1, 2012• 1 citation
Publisher

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 2 β/ν = 1.033(5) and γ/ν = 1.967(5), confirming the hyperscaling relations.

DOI
10.3938/jkps.61.1194

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We improve the theoretical estimates of the critical exponents for the three-dimensional XY universality class. We fine alpha=-0.0146(8), gamma =1.3177(5), nu =0.671 55(27), eta =0.0380(4), beta =0.3485(2), and delta =4.780(2). We observe a discrepancy with the most recent experimental estimate of alpha; this discrepancy calls for further theoretical and experimental investigations. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods, and high-temperature expansions. Two improved models (with suppressed leading scaling corrections) are selected by Monte Carlo computation. The critical exponents are computed from high-temperature expansions specialized to these improved models. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine the specific-heat amplitude ratio.