Quantum and classical statistical mechanics of the sinh-Gordon equation

Abstract

The authors give two fundamental methods for quantum or classical free energies of integrable models. Periodic boundary conditions induce an integral equation for classically allowed momenta. Generalisations of the Berthe ansatz and a method of functional integration on the classical action in action-angle variables follow, giving identical (Bose-Fermi equivalent) results. For sinh-Gordon the Bose classical limits agree with the transfer integral method.