The odd eight-vertex model

Details The odd eight-vertex model The odd eight-vertex model

2003-03-17

arxiv.org/abs/cond-mat/0303303v1

J. Sta. Phys. 116, 67-78 (2004).

Physics

Condensed Matter

Statistical Mechanics

13 pages, 5 figures, dedicated to Elliott H. Lieb on the occasion of his 70th birthday

Scientific paper

10.1023/B:JOSS.0000037206.47155.

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.

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