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Journal of Physics C Solid State Physics

Critical exponents of the modified F model

Herm Jan Brascamp, H Kunz, Fa Yueh Wu

Published Apr 12, 1973• 11 citations
Publisher

Abstract

Critical exponents of an eight-vertex model, the modified F model, are obtained. The results beta = 1 / 4 , gamma = gamma '= 3 / 2 , eta = 1 / 2 , nu = nu '=1 together with the established indices alpha = alpha '=0 obey the scaling relations.
DOI
10.1088/0022-3719/6/7/003

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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.