We show that the thermodynamic properties of the quantum sine-Gordon system in the zero-charge sector can be found from the appropriate limit of the Takahashi-Suzuki Bethe ansatz analysis of the $\mathrm{XYZ}$ spin chain. We prove that the rather complex criteria for allowed states in thermodynamic sums in that analysis correspond simply to including only states with normalizable wave functions. The behavior of the $\mathrm{XYZ}$ phase-shift function in the sine-Gordon limit is discussed.

• Received 11 May 1981

DOI:https://doi.org/10.1103/PhysRevB.24.2634