The lattice quantum Sine-Gordon model

K Babu Joseph, V. C. Kuriakose

Satoshi Takada, Susumu Misawa

M. Ishikawa, Kazuo Hida

The thermodynamics is studied for two exactly soluble models by means of the Bethe ansatz method: the lattice quantum sine-Gordon model and the lattice massive Thirring model proposed by Izergin and Korepin (1981-82), and Weiss and Schotte (1983), respectively. The specific heat is analysed for each of these models as regards the effect of the cut-off parameter. The classical limit of the free energy is also discussed for the lattice quantum Sine-Gordon model.

Mariana Malard

Kazuo Sasaki

The Bethe-ansatz (BA) equation for the classical sine-Gordon (SG) thermodynamics is shown to reduce to the one for the classical Toda lattice within two approximations; the phonon-phonon interactions are neglected (the harmonic phonon) and solitons are treated nonrelativistically. Within these approximations the solitons in the SG model correspond to the particles in the Toda lattice. Making use of an analytical solution of the BA equation for the classical Toda lattice due to Opper, we obtain an analytical solution of the approximate SG equation. We propose also a similar approximate BA equation for the ${\ensuremath{\varphi}}^{4}$ model, although the ${\ensuremath{\varphi}}^{4}$ model does not have the BA equation for the classical thermodynamics.

Alexander A. Ovchinnikov

We study the local lattice integrable regularization of the Sine-Gordon model written down in terms of the lattice Bose-operators. We show that the local spin Hamiltonian obtained from the six-vertex model with alternating inhomogeneities in fact leads to the Sine-Gordon in the low-energy limit. We show that the Bethe Ansatz results for this model lead to the correct general relations for different critical exponents of the coupling constant.