Duality and finite size effects in six vertex models

M. Karowski

Chris J. Hamer

Anatoli G. Izergin

Jae Dong Noh, Doochul Kim

Finite-size corrections to the energy levels of the asymmetric six-vertex model transfer matrix are considered using the Bethe ansatz solution for the critical region. The nonuniversal complex anisotropy factor is related to the bulk susceptibilities. The universal Gaussian coupling constant g is also related to the bulk susceptibilities as g=2${\mathit{H}}^{\mathrm{\ensuremath{-}}1/2}$/\ensuremath{\pi}, H being the Hessian of the bulk free energy surface viewed as a function of the two fields. The modular covariant toroidal partition function is derived in the form of the modified Coulombic partition function which embodies the effect of incommensurability through two mismatch parameters. The effect of twisted boundary conditions is also considered. \textcopyright{} 1996 The American Physical Society.

G I Watson

T S Tavares, G A P Ribeiro, V. E. Korepin

We study the dependence of entropy [per lattice site] of six-vertex model on boundary conditions. We start with lattices of finite size and then proceed to thermodynamic limit. We argue that the six-vertex model with periodic, anti-periodic and mixed boundary conditions produce the same free-energy in the thermodynamic limit. We have found fixed boundary conditions such that the entropy varies continuously from zero to its value for periodic boundary condition. We have also shown that the physical quantities of the six-vertex model at the isotropic point does not change in the case of singular toroidal boundary.