The Bethe ansatz variational approach to the thermodynamics of the massive Thirring-sine-Gordon model in the attractive coupling regime and in the zero-change sector is discussed in detail.
A new method based on the S-matrix factorization is developed for the thermodynamics of the massive Thirring model. The method can be applied to any charge sector and coupling constant. In the zero-charge sector, the present theory reproduces all the Bethe-Ansatz-theory results in the attractive-coupling regime, and agrees with a perturbation calculation in the repulsive-coupling regime.
Using the Bethe-ansatz method we analyze the thermodynamic properties of the massive Thirring model in the zero-charge-sector attractive case, including the "charged vacuum" excitations introduced by Korepin. The energy of these excitations is calculated as a function of momentum and temperature and agrees with Korepin's results at T=0. The specific heat is presented and shown to vary smoothly for the whole range of coupling in the attractive regime.
The Bethe-ansatz equations for the thermodynamic properties of the quantum sine-Gordon systems are derived in the zero-charge-sector attractive case. For rational values of the coupling parameter $\frac{\ensuremath{\mu}}{\ensuremath{\pi}}$ these reduce to a finite set, solved here numerically for $\ensuremath{\mu}=[\frac{(n\ensuremath{-}1)}{n}]\ensuremath{\pi}$, for several values of n, to give the specific heat as a function of temperature. The "soliton" contribution peaks at $\ensuremath{\simeq}0.4$ soliton masses for $\ensuremath{\mu}=\frac{4}{5}\ensuremath{\pi}$, shifting downward for higher $\ensuremath{\mu}$. A detailed analysis of the sine-Gordon limit of the XYZ spin chain is presented, and a non-Lorentz-invariant feature of that limit is noted.