New solvable cases for the eight-vertex model

J. Zittartz

K. Fabricius, Barry M. McCoy

Klaus Fabricius, Barry M. McCoy

R. J. Baxter

Abstract Any planar set of intersecting straight lines forms a four-coordinated graph, or ‘lattice’, provided no three lines intersect at a point. For any such lattice an eight-vertex model can be constructed. Provided the interactions satisfy certain constraints (which are in general temperature-dependent), the model can be solved exactly in the thermodynamic limit, its local properties at a particular site being those of a related square lattice. A particular case is a solvable model on the Kagomé lattice. It is shown that this model includes as special cases many of the models in statistical mechanics that have been solved exactly, notably the square, triangular and honeycomb Ising models, and the square eight-vertex model. Some remarkable equivalences between correlations on different lattices are also established.

Vladimir V. Bazhanov, Vladimir V. Mangazeev

Yas-Hiro Quano

The eight-vertex model at the reflectionless points is considered on the basis of Smirnov's axiomatic approach.Integral formulae for form factors of the eight-vertex model can be obtained in terms of those of the eight-vertex SOS model, by using vertex-face transbrma- tion.The resulting formulae have very simple forms at the reflectionless points, and suggest us the free field representation of type II vertex operators in the eight-verterc model.