Statistical Mechanics of Some Co-Operative Phenomena

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Abstract

THERE are a number of co-operative phenomena associated With specific heat singularities for which the technical mathematical problems are formally similar. These include the Ising model of a ferromagnetic, the theory of regular binary solid solutions, and the order–disorder transitions in alloys. Many approximations have been devised for treating these problems, and as a typical example we may quote the Bethe approximation1. It was at first considered that these approximations provided a satisfactory account of the thermodynamics of the problems. Recently, however, the exact solution of a particular problem by Onsager2,3 has shown that the standard approximations are unreliable in the neighbourhood of the singularity, and has focused attention on exact solutions.

References

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    Lassetre, E. N., and Howe, J. P., J. Chem. Phys., 9, 747, 801 (1941).

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DOMB, C. Statistical Mechanics of Some Co-Operative Phenomena. Nature 163, 775–776 (1949) doi:10.1038/163775a0

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