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

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 Cc, for the susceptibility and, ƒ1c, 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, θc, 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(ƒ1−)2 = 0.0965 ± 2, Ccδ/(Bδ−1C+)1/δ = 0.93 ± 25, and (C+/Cc)(ƒ1c/ƒ1+)2−η = 1.17 ± 2, where B, ƒ1−, and C+ are the amplitudes of the spontaneous magnetization, and (second moment) correlation length, and of the susceptibility above Tc