Some New Integrable Models in Field Theory and Statistical Mechanics

Hector J. de Vega

William P. Orrick

Mario Rasetti

Miki Wadati, Yasuhiro Akutsu

Development in the theory of solvable (integrable) models is reviewed. It covers from basic knowledge on completely integrable systems to recent work by the authors. First, soliton theory is briefly summarized. Through the inverse scattering method and its quantum extension, a central concept, commuting transfer matrices, and a key relation, the Yang-Baxter relation, are introduced. Second, it is shown that there exists at least ∞ × ∞ number of solvable models in two-dimensional statistical mechanics. Third, quantum spin chains corresponding to solvable statistical mechanical models are discussed. In particular, finite temperature extension of Baxter's formula is given. Fourth, a new approach is presented to the classification problem of knots and links. It is shown that link polynomial, topological invariant for knots and links, can be associated with any solvable model in statistical mechanics. In the presentation, universality of the soliton picture in field theory, spin systems and statistical mechanics is observed.

Hector J. de Vega

Peter Bouwknegt

The conference brought together leading researchers at the interface between statistical mechanics and quantum field theory, which is, and has been, a very rich, dynamic and useful area of theoretical physics. The following topics that are of very active and current interest were covered: the study of renormalization group flows between field theories using the methods of quantum integrability, S-matrix theory and the thermodynamic Bethe Ansatz; impurity problems approached both from the point of view of conformal field theory and quantum integrability; the Kondo effect and quantum wires; solvable models with 1/r2 interactions (Haldane-Shastri models); Yangian symmetries in 1/r2 models and in conformal field theories; correlation functions in integrable 1+1 field theories; integrability in three dimensions; conformal invariance and the quantum hall effect; supersymmetry in statistical mechanics; and relations to two-dimensional Yang-Mills and QCD.