Document Type
Article
Original Publication Date
1982
Journal/Book/Conference Title
Journal of Applied Physics
Volume
53
Issue
3
DOI of Original Publication
10.1063/1.330664
Date of Submission
October 2015
Abstract
We use an effective field model which explicitly incorporates correlations to determine the critical temperatures for Ising ferromagnets on the common lattices. We specifically retain only the first nontrivial odd correlation function, i.e., the triplet correlation function, while neglecting higher order correlations. Within this approximation, assuming the equivalence of triplet correlations involving both central and noncentral sites in the nearest neighbor cluster yields values for the critical temperature below the Bethe approximations for z⩾4. Likewise, assuming the inequivalence of triplet correlations involving the central and noncentral sites yields values of the critical temperature only slightly higher than the Bethe approximation for z⩾4. For lattices with four‐ and six‐fold coordination this equivalence and inequivalence of triplet correlation functions is sufficient to cause the critical temperatures to approach their two‐ and three‐dimensional values. For instance, for quadratic lattices we obtain values for the critical temperature of 2.5284 and 2.9796 as compared to the exact and series results of 2.2692 and 2.7044 for the simple quadratic and diamond lattices, respectively, and the Bethe approximation of 2.8854.
Rights
Taggart, G. B. Effective field model for Ising ferromagnets: Influence of triplet correlations. Journal of Applied Physics 53, 1907 (1982). Copyright © 1982 AIP Publishing LLC.
Is Part Of
VCU Physics Publications
Comments
Originally published at http://dx.doi.org/10.1063/1.330664