Classical sine-Gordon limit of massive-Thirring-model thermodynamics

It has been shown numerically by Chung that in the classical sine-Gordon limit the low-temperature thermodynamic properties of the massive Thirring model, as calculated using the Bethe ansatz, correspond to those of a free-phonon gas. We give an analytic derivation of this result and find simple expressions for the finite-temperature "excitation-spectrum" functions, and discuss their physical significance.