The odd eight-vertex model

TL;DR

This paper introduces the odd 8-vertex model on a lattice, establishes its equivalence to a staggered 8-vertex model, and solves it under free-fermion conditions, revealing no phase transitions for positive weights.

Contribution

It demonstrates the equivalence of the odd 8-vertex model to a staggered model and provides its exact solution under free-fermion conditions, connecting it to known models.

Findings

The odd 8-vertex model is equivalent to a staggered 8-vertex model.

The model is exactly solvable under free-fermion conditions.

No phase transitions occur in the positive weight regime.

Abstract

We consider a vertex model on the simple-quartic lattice defined by line graphs on the lattice for which there is always an odd number of lines incident at a vertex. This is the odd 8-vertex model which has eight possible vertex configurations. We establish that the odd 8-vertex model is equivalent to a staggered 8-vertex model. Using this equivalence we deduce the solution of the odd 8-vertex model when the weights satisfy a free-fermion condition. It is found that the free-fermion model exhibits no phase transitions in the regime of positive vertex weights. We also establish the complete equivalence of the free-fermion odd 8-vertex model with the free-fermion 8-vertex model solved by Fan and Wu. Our analysis leads to several Ising model representations of the free-fermion model with pure 2-spin interactions.