Integrable Models Away from Criticality

J C Anglès d'Auriac

The three-state Potts model on a Kagomé lattice with three equal coupling constants is studied in the vicinity of the critical point and away from it by means of Random Matrix Theory. Circumstantial evidence indicating that at the critical point it is integrable is given.

N. M. Bogoliubov, Anatoli G. Izergin, V. E. Korepin

Giuseppe Mussardo

Abstract In this chapter we present the S-matrix theory of two-dimensional integrable models. This leads, in particular, to the exact spectrum of the massive excitations away from the critical point. From a mathematical point of view, the two-dimensional nature of the systems and their integrability are the crucial features that lead to important simplifications of the formalism and its successful application. It is worth mentioning that, initially developed to overcome the obstacles encountered by quantum field theory in dealing with the strong interactions of the hadronic particles1 (such as protons, neutrons, or pions), the S-matrix has achieved its most beautiful intellectual triumph in the analysis of the two-dimensional statistical models away from criticality, particularly when they are described by integrable theories. These significant developments have been pioneered by A.B. Zamolodochikov.

Costas John Efthimiou

Jenő Sólyom, JUSSI TIMONEN

Composite spin models are constructed such that, by varying two parameters, they interpolate between the spin-(1/2 antiferromagnetic Heisenberg chain and a number of spin-1 models. These include the usual Heisenberg model, the integrable spin-1 model, and the model with an exact valence-bond ground state. Finite-chain calculations are performed on the composite spin model to study its criticality, and to find if the integrable spin-1 model is a multicritical point with a finite gap generated away from it. We find indications for an extended gapless region.

JUSSI TIMONEN, Yu Chen, R. Bullough