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

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.

Text of the 1999 Heineman Prize address given March 24 at the Centenial Meeting of the American Physical Society in Atlanta 20 pages in latex, references added and typos corrected

References in corpus (1)

• The perturbations ${\varphi }_{2,1}$ and ${\varphi }_{1,5}$ of the minimal models $M(p,p^{\prime })$ and the trinomial analogue of Bailey's lemma

Cited by in corpus (4)

• Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an algebraic approach to the Askey scheme of orthogonal polynomials
• Chiral Potts Rapidity Curve Descended from Six-vertex Model and Symmetry Group of Rapidities
• Multi-critical absorbing phase transition in a class of exactly solvable models
• Algebraic Geometry and Physics