ABSTRACT
We have mentioned in §1.5 the shattering blow which Onsager's exact calculations for a two-dimensional Ising model delivered to the classical theories, and the challenge it posed in relation to critical behaviour. But Onsager's work had much wider ramifications since detailed aspects of his calculations stimulated important new areas of research and progress. His topological interpretation of the duality transformation discovered by Kramers and Wannier greatly extended its scope, and soon led, in conjunction with his formulation of the star-triangle transformation, to exact solutions for other twodimensional lattices (see e.g. Domb 1960 pp. 211-20). The star-triangle transformation itself initiated a search which revealed other useful transformations of a similar kind (see e.g. Syozi 1972). The simplification of the calculations by the use of spinors led to the discovery of other simplified methods of calculation each of which had its own specific advantages (Temperley 1972, Schultz, Mattis and Lieb 1964). More remotely the existence of exact solutions to the Ising model in two dimensions suggested that other realistic models might give rise to exact solutions. Over 20 years elapsed before a breakthrough occurred (Lieb 1967). Subsequently this area of research has generated results of great interest and importance (Baxter 1982).
