Bethe-ansatz quantum sine-Gordon thermodynamics. Finite-temperature excitation spectrum

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Abstract
The thermal renormalization of the Bethe-ansatz excitation spectrum for the sine-Gordon system is presented. For the soliton mass, the results agree closely with those of Maki and Takayama over a significant temperature range, but the sudden decrease in mass they predict near a particular temperature is not found. For the Bethe-ansatz excitation corresponding to the phonon at zero temperature, the rest mass changes rapidly as the temperature increases, even near the classical limit. This suggests that at finite temperature this excitation (the one-string) no longer corresponds to the physical phonon.