The near-critical planar FK-Ising model
Abstract
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 (e.g., in the one introduced in [Gri95]), as one raises near , 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.
Keywords
Cite
@article{arxiv.1111.0144,
title = {The near-critical planar FK-Ising model},
author = {Hugo Duminil-Copin and Christophe Garban and Gábor Pete},
journal= {arXiv preprint arXiv:1111.0144},
year = {2015}
}
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