The eight-vertex model via dimers (Paul Melotti, Université de Fribourg)

25.05.2020 15:15 – 16:15

The eight-vertex model is an ubiquitous description that generalizes several spin systems, the more common six-vertex model, Ashkin-Teller models, and others. In a special "free-fermion" regime, it is known since the work of Fan, Lin, Wu in the late 60s that the model can be mapped to non-bipartite dimers. However, no general theory is known for dimers in the non-bipartite case, contrary to the extensive rigorous description of Gibbs measures by Kenyon, Okounkov, Sheffield for bipartite dimers. In this talk I will show how to transform these non-bipartite dimers into bipartite ones, on generic planar graphs. I will mention a few consequences: computation of long-range correlations, criticality and critical exponents, and their "exact" application to Z-invariant regimes on isoradial graphs.

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Séminaire "Mathématique Physique"

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