Symmetry relations in the sixteen-vertex model

Marc Bellon, J.-M. Maillard, C.-M. Viallet

G I Watson

I. G. Korepanov

S. Boukraa, J.-M. Maillard

A classification of the subcases of the sixteen-vertex model compatible with the infinite symmetry group generated by the inversion relations of the model is performed. The elliptic parameterization of these models is recalled, emphasizing the subvarieties of the parameter space for which this parameterization degenerates into a rational one. This situation corresponds to the vanishing of some discriminant and is deeply related to the critical and disorder manifolds for these models. We concentrate on subcases of the sixteen-vertex model for which factorizations of this discriminant occur, allowing further exact calculations.

Vladimir V. Bazhanov, Vladimir V. Mangazeev

C.S. Hsue, Ken‐Yu Lin, Fa Yueh Wu

An eight-vertex model with staggered (site-dependent) vertex weights is considered. The model is an extension of the usual one with translationally invariant weights and contains sixteen independent vertex weights. From its Ising representation it is seen that there are actually only eleven independent parameters. After discussing some general symmetry properties of this model, we consider in detail the soluble case of a free-fermion model. We find that the staggered free-fermion model may exhibit up to three phase transitions. Generally the specific heat has logarithmic singularities, expect in some special cases it has an exponent $\ensuremath{\alpha}=\frac{1}{2}$ and the system is frozen below a unique transition point. Conditions for these special cases are given.