On co-operative effects in finite assemblies

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Abstract
A comparison is undertaken of graphs which contribute to the partition functions of an infinite assembly and a finite assembly wrapped on a torus. This leads to an order of magnitude estimate of the maximum in the specific heat of finite two- and three-dimensional Ising models. It is found that for a normal size assembly and for a single crystal the specific heat deviates from its limiting value for an infinite assembly when the temperature is within a factor of about 10-7 of the Curie temperature. This figure would be modified to perhaps 10-6 for the usual multi-grain structure. A similar discussion is undertaken for the magnetic susceptibility above the Curie temperature.

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