Hugo Duminil-Copin, Christophe Garban, Gábor Pete
Published 2011-11-01, updated 2014-02-13Version 4
We study the near-critical FK-Ising model. First, a determination of the correlation length defined via crossing probabilities is provided. Second, a phenomenon about the near-critical behavior of FK-Ising is highlighted, which is completely missing from the case of standard percolation: in any monotone coupling of FK configurations $\omega_p$ (e.g., in the one introduced in [Gri95]), as one raises $p$ near $p_c$, the new edges arrive in a self-organized way, so that the correlation length is not governed anymore by the number of pivotal edges at criticality.
Comments: 34 pages, 8 figures. This is a streamlined version; the previous one contains more explanations and additional material on exceptional times in FK models with general $q$. Furthermore, the statement and proof of Theorem 1.2 have slightly changed
Journal: Comm. Math. Phys. 326 (2014), no. 1, 1--35
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Correlation length of two-dimensional random field Ising model via greedy lattice animal
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