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Divergence of the correlation length for critical planar FK percolation with 1≤q≤4 via parafermionic observables

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Published in Journal of Physics. A, Mathematical and Theoretical. 2012, vol. 45, p. 26
Abstract Parafermionic observables were introduced by Smirnov for planar FK percolation in order to study the critical phase $(p,q)=(p_c(q),q)$. This article gathers several known properties of these observables. Some of these properties are used to prove the divergence of the correlation length when approaching the critical point for FK percolation when $1le qle 4$. A crucial step is to consider FK percolation on the universal cover of the punctured plane. We also mention several conjectures on FK percolation with arbitrary cluster-weight $q>0$.
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arXiv: 1208.3787
Note 26 pages
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DUMINIL-COPIN, Hugo. Divergence of the correlation length for critical planar FK percolation with 1≤q≤4 via parafermionic observables. In: Journal of Physics. A, Mathematical and Theoretical, 2012, vol. 45, p. 26. https://archive-ouverte.unige.ch/unige:30934

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Deposited on : 2013-11-05

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