Exact Results for Thermodynamics of the Classical Field Theories: Sine- and Sinh-Gordon Models

TL;DR

This paper uses exact operator expectation values to analyze the thermodynamics of sine- and sinh-Gordon models, revealing a maximum in specific heat below the Kosterlitz-Thouless transition and instability in the sinh-Gordon model at strong coupling.

Contribution

It provides the first exact calculation of the specific heat for these classical field theories using recent operator expectation results.

Findings

Sine-Gordon model's specific heat peaks below the Kosterlitz-Thouless transition.

Sinh-Gordon model is thermodynamically unstable at strong coupling.

Temperature dependence of specific heat in the incommensurate phase of sine-Gordon.

Abstract

Using the recently obtained exact results for the expectation values of operators in the sine- and sinh-Gordon models [A. B. Zamolodchikov and S. Lukyanov, Nucl. Phys. B{\bf 493}, 571 (1997), V. Fateev, S. Lukyanov, A. B. Zamolodchikov and Al. B. Zamolodchikov, Phys. Lett. B{\bf 406}, 83 (1997)] we calculate the specific heat of the corresponding two dimensional Euclidean (classical) models. We show that the temperature dependence of the specific heat of the sine-Gordon model, in the commensurate phase, has a maximum well below the Kosterlitz-Thouless transition and that the sinh-Gordon model is thermodynamically unstable in the strong coupling regime. We give also the temperature dependence of the specific heat in the incommensurate phase of the sine-Gordon model.