An Improvement in the Spherical Approximation of an Ising Spin System

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  • Improvement in the Spherical Approximat

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Rewriting the partition function of an Ising system as a multiple integral, dividing the integration space by a set of concentric spherical surfaces and sets of parallel planes into small domains, averaging separately the two factors constituting the integrand of the multiple integral over each of these domains, and replacing the two factors by their respective averages, logarithm of the partition function per spin is given by the extremum of a function with respect to a complex variable and a number of real variables. The specific heat curve of an Ising square lattice obtained by the present method is compared with those by the exact method, the spherical approximation and the mean field approximation.

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