Two - Dimensional king Correlations : The SMJ Analysis

6.6). In [3, 31, 321 Wu, McCoy, Tracy, and Barouch (WMTB) discovered that the scaled two point functions for the two-dimensional Ising model are expressible in terms of a Painled function of the third kind. This discovery was made by using results from the thesis of Myers [21] (which was in part based upon earlier work by Latta [16]) who established a connection between a linear integral equation arising in the problem of electromagnetic scattering from a strip and a differential equation of Painleve type. A summary of the Latta-Myers method can be found in Appendix B of WMTB. Later in [ 191 McCoy, Tracy, and Wu improved the mathematical foundations of the two point function analysis, and developed connection formulas for a family of solutions to the Painleve equation. In an impressive series of papers, SMJ generalized the two point function result to the higher correlations, and these authors found what we believe is certainly the natural setting for these results. For an overview of this work, the reader will find [12] helpful. They were aware that all the Painleve transcendents arise naturally in the integration of the simplest of the Schlesinger equations for monodromy preserving deformations of linear