The 1999 Heineman Prize Address- Integrable models in statistical mechanics: The hidden field with unsolved problems

TL;DR

This paper reviews three decades of progress in integrable models in statistical mechanics, highlighting key discoveries, unresolved problems, and the field's limited visibility despite its significant mathematical and physical insights.

Contribution

It provides a comprehensive overview of major advances and unsolved problems in integrable models, emphasizing their importance and the need for further research.

Findings

Discovery of non-linear differential equations for Ising correlations

Development of the theory of random impurities

Use of Rogers-Ramanujan identities in statistical models

Abstract

In the past 30 years there have been extensive discoveries in the theory of integrable statistical mechanical models including the discovery of non-linear differential equations for Ising model correlation functions, the theory of random impurities, level crossing transitions in the chiral Potts model and the use of Rogers-Ramanujan identities to generalize our concepts of Bose/Fermi statistics. Each of these advances has led to the further discovery of major unsolved problems of great mathematical and physical interest. I will here discuss the mathematical advances, the physical insights and extraordinary lack of visibility of this field of physics.