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The three-dimensional Ising model revisited numerically

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  • Liu, Andrea J.
  • Fisher, Michael E.

Abstract

Several basic universal amplitude ratios are studied afresh for three-dimensional nearest-neighbor Ising models. In revising earlier work, modern estimates of the critical temperature and exponents are used in conjunction with biased inhomogeneous differential approximants to extrapolate the longest available series expansions to find the critical amplitudes: C± for the susceptibility χ; ƒ1± for the correlation length ζ1; A± for the specific heat C(T); and B for the spontaneous magnetization M0. We find C+C- = 4.95±0.15, ƒ1+ƒ1- = 1.960±0.01, A+A- = 0.523±0.009, αA+C+B+ = 0.0581±0.0010, while αA+ (ƒ1+)3 verifies hyperuniversality to within ±0.8%. A method for calculating amplitude ratios which allows for corrections to scaling yields estimates for C+C- and ƒ1+ƒ1- in excellent agreement with those derived from the individual amplitudes. Finally, explicit formulae are given for the numerical evaluation of χ(T), ζ1(T), C(T) and M0(T) over the full temperature range from criticality to T=0 and ∞; corresponding plots and convenient near-critical representations are also presented.

Suggested Citation

  • Liu, Andrea J. & Fisher, Michael E., 1989. "The three-dimensional Ising model revisited numerically," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 156(1), pages 35-76.
    • Handle: RePEc:eee:phsmap:v:156:y:1989:i:1:p:35-76
    DOI: 10.1016/0378-4371(89)90109-X
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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. Albright, Elizabeth Gerber & Albright, Robert J., 1985. "The economic impact of uncertainties associated with energy-saving technologies," Energy, Elsevier, vol. 10(5), pages 631-634.
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