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Journal of Physics C Solid State Physics

The finite temperature properties of the massive Thirring model and the quantum sine-Gordon model

Masatoshi Imada, Kazuo Hida, M. Ishikawa

Published Jan 10, 1983• 27 citations
Publisher

Abstract

The thermodynamics of the massive Thirring model is discussed with the help of the Bethe Ansatz approach in a way different from Fowler and Zotos (1982). In particular a finite Debye cut-off is introduced to investigate effects of the lattice discreteness. The specific heat seems to have a structure as a sum of the Debye-type specific heat and a 'soliton' peak, when the authors take into account the relation of the massive Thirring model to the quantum sine-Gordon model. The finite temperature excitations are calculated. The excitation energy proposed by Fowler and Zotos is shown to have significance which is insensitive to the way of formulation.

DOI
10.1088/0022-3719/16/1/008

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The thermodynamics of the massive Thirring model is discussed with the help of the Bethe Ansatz approach in a way different from Fowler and Zotos (1982). In particular a finite Debye cut-off is introduced to investigate effects of the lattice discreteness. The specific heat seems to have a structure as a sum of the Debye-type specific heat and a 'soliton' peak, when the authors take into account the relation of the massive Thirring model to the quantum sine-Gordon model. The finite temperature excitations are calculated. The excitation energy proposed by Fowler and Zotos is shown to have significance which is insensitive to the way of formulation.
For the quantum sine-Gordon--massive Thirring model at finite temperature, the relationship between the Bethe ansatz ``elementary excitations'' and physical excitations of the system is examined. The thermodynamic equations are written in terms of a set of dressed particles in the general case. We find that the recently predicted soliton mass discontinuity (on varying coupling strength at finite temperature) is not a real effect--the function exhibiting the discontinuity does not correspond to the mass of the soliton.
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 nnn, 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\mathrm{XYZ}XYZ spin chain is presented, and a non-Lorentz-invariant feature of that limit is noted.