Soliton statistical mechanics: Thermodynamic limits for quantum and classical integrable models

R. Bullough, D. J. Pilling, JUSSI TIMONEN

R. Bullough, D. J. Pilling, JUSSI TIMONEN +2 more

Nikos Theodorakopoulos, N. C. Bacalis

We examine the statistical mechanics of the classically integrable Ishimori-Faddeev-Haldane lattice spin model. Thermodynamic properties can be exactly described in terms of an interacting soliton gas. Our semiclassical scheme can be used to calculate the low-temperature thermodynamics of the S=1/2 Heisenberg chain, in very good agreement with recent numerical calculations based on the quantum-mechanical Bethe ansatz.

Alan H. Luther

S. G. Chung

This paper reviews soliton theories for classical statistical mechanics of the massive-Thirring-sine-Gordon model. These theories attempt not only to reproduce the classical transfer matrix method result but also to provide thermodynamic information about exact nonlinear excitations of the model. Three theories are discussed. Firstly, the soliton–gas phenomenology which is successful in the Toda lattice is shown to be not even approximately correct for the sine-Gordon model. This breakdown is due to the incorrect counting of the number of degrees of freedom. Secondly, the soliton–phonon theory which reproduces the WKB result is also shown to be not exact. This non-exactness is ascribed to the fact that the nonlinear phonons are not exact elementary excitations in the model. Thirdly, a non-gas phenomenological soliton–breather theory is derived as a classical limit of quantum statistical mechanics of the model. The exactness of the last theory is demonstrated through an accurate numerical analysis of its basic equations.

R. Bullough, D. J. Pilling, JUSSI TIMONEN