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Article Dans Une Revue Communications in Mathematical Physics Année : 2021

The Free-Fermion Eight-Vertex Model: Couplings, Bipartite Dimers and Z-Invariance

Résumé

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 et al. (Probab Theory Relat Fields 174:235–305, 2019), 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.

Dates et versions

hal-04031203 , version 1 (15-03-2023)

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Citer

Paul Melotti. The Free-Fermion Eight-Vertex Model: Couplings, Bipartite Dimers and Z-Invariance. Communications in Mathematical Physics, 2021, 381 (1), pp.33-82. ⟨10.1007/s00220-020-03901-2⟩. ⟨hal-04031203⟩
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