Statistics of the simple cubic lattice

Both the Ising theory of ferromagnetism and the theory of regular solutions are concerned with systems arranged on a lattice and make the assumption that each system interacts only with its nearest neighbours. Mathematically, there is a close parallel between the two problems (see, for instance, Rushbrooke ( 1 )). In the first half of this present paper the partition functions for these two problems are examined in some detail. Power series expansions of the partition function of the Ising model, valid for low and high temperatures, are obtained. The terms obtained in the power series have been analysed and approximate numerical results obtained. It is hoped to publish these in a second paper.

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