The free-fermion eight-vertex model via dimers
Paul Melotti (Université Paris Saclay)
Abstract: The eight-vertex model is an useful description that generalizes several spin systems, as well as the more common six-vertex model, 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.
condensed mattermathematical physics
Audience: researchers in the topic
Quantum Matter meets Maths (IST, Lisbon)
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Organizers: | João P. Nunes, Jose Mourao*, Pedro Ribeiro, Roger Picken, Vítor Rocha Vieira |
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