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 staggered8-vertex model. Using this equivalence we deduce the solution of the odd8-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 thefree-fermion model with pure 2-spin interactions.
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Wu, F.Y., Kunz, H. The Odd Eight-Vertex Model. Journal of Statistical Physics 116, 67–78 (2004). https://doi.org/10.1023/B:JOSS.0000037206.47155.58
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DOI: https://doi.org/10.1023/B:JOSS.0000037206.47155.58