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.
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Archive for History of Exact Sciences (2009)
Philosophical Magazine (2007)
Physica A: Statistical Mechanics and its Applications (1990)
Il Nuovo Cimento (1949)