Critical correlation-function approximations for the Ising model

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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 M2n(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 Tc 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).