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Journal of Physics C Solid State Physics

The critical correlation function of the Ising model in a magnetic field and below the critical temperature

Mark Bisset

Published Dec 7, 1974• 0 citations
Publisher

Abstract

The critical spin-spin correlation function of the Ising model in a magnetic field and below the critical temperature has been calculated up to and including terms of order epsilon 2.
DOI
10.1088/0022-3719/7/23/005

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In a new theory for the spin one-half Ising ferromagnet, the fourth-order equation is used to provide expressions for the higher-order site-independent correlation functions M 2n (n=3,4,5,...) in terms of the two- and four-spin correlation functions M 2 and M 4 , at the critical point. As an example, the expression for M 6 is M 4 2 /M 2 -9M 2 M 4 -6M 2 3 . These expressions (for up to M 60 ) are applied to the calculation of T c for the SC, BCC, and FCC lattices. The results converge to, at most, 0.755, 0.799, and 0.819 respectively, which are within 2 / 3 % of the accepted results 0.752, 0.794, and 0.816 of Sykes et al. (1972).
Expressions for general correlation functions in Ising ferromagnets are derived in terms of the Lee-Yang theorem. By the use of these expressions, the asymptotic forms of correlation functions in the presence of magnetic field are analyzed, assuming those in the absence of the external field. In particular, the critical indices of spin-spin, energy-density-energy-density, energy-density-spin correlation functions are related with the critical indices of thermal susceptiblity χT0, specific heat, susceptibility χH0, and magnetization. These results agree in form with those predicted by the scaling law approach.