MathPhys Odyssey 2001

This volume is dedicated to Barry M. McCoy on the occasionofhis sixtieth birthday. Barry McCoy has led the research on integrable models in statistical mechanics and quantumfieldtheoryfor morethan 30years. Hisbook,cowrittenwithT.T.Wu, The Two dimensional/sing Model, (HarvardUniversity)containsallthebasic resultsontheIsing model obtained by the early 1970s. However, McCoy'sjointpaper with Wu, Tracy and Barouch, Spin-spin correlation functions for the two-dimensional/sing model: Exact results in the scaling region (Physical Review B13, 316-374, 1976), was a giant step beyond the book. A remarkable connection between the two-point scaling correlation functions and the Painleve transcendents was found. This work made an enormous impact on mathematical physics in the last quarter of the 20th century. It gave the first nontrivial exampleofinteracting field theory in which the Green function can be written explicitly in terms of special functions satisfying nonlinear differential equations. Later in the 1980s, an extensive list of massless field theories was added in the innovation of conformal field theory, in which the Green functions are characterized by linear differential equationsofthe hypergeometric type. However,evenalmost30yearsaftertheirwork, theIsingmodel isessentiallytheunique casewhereall theGreenfunctionsofmassivefield theoryarecharacterizedbynonlinear differential equations.