Universal surface-tension and critical-isotherm amplitude ratios in three dimensions

Abstract

The universal surface-tension and critical-isotherm amplitude ratios are studied numerically for three-dimensional Ising models. Modern estimates of the critical temperature and exponents allow reliable evaluation of the critical surface-tension amplitude, K, using recent Monte Carlo data for the simple cubic lattice. Likewise, the amplitudes C c, for the susceptibility and, ƒ 1 c , for the second-moment correlation length, on the critical isotherm have been re-estimated using existing series expansions. The method of inhomogeneous differential approximants also yields a direct estimate of the correction-to-scaling exponent, θ c, on the critical isotherm which, via scaling, corresponds to the thermal correction exponent θ = 0.55 ± 5 this supports previous estimates and the stronger conclusion θ = 0.54 ± 3. For the universal ratios, we estimate K(ƒ 1 −) 2 = 0.096 5 ± 2, C c δ/(B δ−1C +) 1 δ = 0.93 ± 2 5 , and (C +/C c )(ƒ 1 c /ƒ 1 +) 2−η = 1.17 ± 2 , where B, ƒ 1 −, and C + are the amplitudes of the spontaneous magnetization, and (second moment) correlation length, and of the susceptibility above T c.