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A note on Schramm's locality conjecture for random-cluster models

Hugo Duminil-Copin, Vincent Tassion

24/7/17 Published in : arXiv:1707.07626

In this note, we discuss a generalization of Schramm's locality conjecture to the case of random-cluster models. We give some partial (modest) answers, and present several related open questions. Our main result is to show that the critical inverse temperature of the Potts model on \mathbb Z^r\times(\mathbb Z/2n\mathbb Z)^{d-r} (with r\ge3) converges to the critical inverse temperature of the model on Zd as n tends to infinity. Our proof relies on the infrared bound and, contrary to the corresponding statement for Bernoulli percolation, does not involve renormalization arguments.

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Bounds for OPE coefficients on the Regge trajectory

BV-equivalence between triadic gravity and BF theory in three dimensions

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