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

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  • Zinn, Shun-yong
  • Fisher, Michael E.

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 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+)1δ = 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.

Suggested Citation

  • Zinn, Shun-yong & Fisher, Michael E., 1996. "Universal surface-tension and critical-isotherm amplitude ratios in three dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 226(1), pages 168-180.
    • Handle: RePEc:eee:phsmap:v:226:y:1996:i:1:p:168-180
    DOI: 10.1016/0378-4371(95)00382-7
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    1. Hohenberg, Paul M., 1976. "European Peasants and Their Markets: Essays in Agrarian Economic History. Edited by William N. Parker and Eric L. Jones. Princeton, N.J.: Princeton University Press, 1975. Pp. 366. $16.50," The Journal of Economic History, Cambridge University Press, vol. 36(3), pages 782-784, September.
    2. Ramos-Gómez, F. & Widom, B., 1980. "Noncritical interface near a critical end point II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 104(3), pages 595-620.
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