Critical correlation-function approximations for the Ising model

Abstract

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 M₂ and M₄, at the critical point. As an example, the expression for M₆ is M₄²/M₂-9M₂M₄-6M₂³. These expressions (for up to M₆₀) 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).