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The free-fermion eight-vertex model: couplings, bipartite dimers and Z-invariance

Abstract : We study the eight-vertex model at its free-fermion point. We express a new "switching" symmetry of the model in several forms: partition functions, order-disorder variables, couplings, Kasteleyn matrices. This symmetry can be used to relate free-fermion 8V-models to free-fermion 6V-models, or bipartite dimers. We also define new solution of the Yang-Baxter equations in a "checkerboard" setting, and a corresponding Z-invariant model. Using the bipartite dimers of Boutillier, de Tilière and Raschel [14], we give exact local formulas for edge correlations in the Z-invariant free-fermion 8V-model on lozenge graphs, and we deduce the construction of an ergodic Gibbs measure.
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https://hal.archives-ouvertes.fr/hal-01917153
Contributor : Paul Melotti Connect in order to contact the contributor
Submitted on : Wednesday, October 28, 2020 - 5:25:52 PM
Last modification on : Monday, December 14, 2020 - 5:38:14 PM

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  • HAL Id : hal-01917153, version 2

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Paul Melotti. The free-fermion eight-vertex model: couplings, bipartite dimers and Z-invariance. 2020. ⟨hal-01917153v2⟩

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