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Journal articles
The self-dual point of the two-dimensional random-cluster model is critical for $q\geq 1$
Abstract : We prove a long-standing conjecture on random-cluster models, namely that the critical point for such models with parameter $q\geq1$ on the square lattice is equal to the self-dual point $p_{sd}(q) = \sqrt q /(1+\sqrt q)$. This gives a proof that the critical temperature of the $q$-state Potts model is equal to $\log (1+\sqrt q)$ for all $q\geq 2$. We further prove that the transition is sharp, meaning that there is exponential decay of correlations in the sub-critical phase. The techniques of this paper are rigorous and valid for all $q\geq 1$, in contrast to earlier methods valid only for certain given $q$. The proof extends to the triangular and the hexagonal lattices as well.
Cited literature [28 references]
https://hal-ens-lyon.archives-ouvertes.fr/ensl-00495872
Contributor : Vincent Beffara <>
Submitted on : Saturday, January 20, 2018 - 5:33:26 PM
Last modification on : Wednesday, November 20, 2019 - 8:11:19 AM
Document(s) archivé(s) le : Thursday, May 24, 2018 - 6:23:50 AM
Contributor : Vincent Beffara <>
Submitted on : Saturday, January 20, 2018 - 5:33:26 PM
Last modification on : Wednesday, November 20, 2019 - 8:11:19 AM
Document(s) archivé(s) le : Thursday, May 24, 2018 - 6:23:50 AM
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BD:fkcriticalpoint.pdf
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