Crossing probabilities in topological rectangles for the critical planar\n FK-Ising model

2013/12/30 by Dmitry Chelkak, Hugo Duminil‐Copin, Chelkak, Dmitry +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1312.7785

openalex publication_date 2013/12/30 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We consider the FK-Ising model in two dimensions at criticality. We obtain\nbounds on crossing probabilities of arbitrary topological rectangles, uniform\nwith respect to the boundary conditions, generalizing results of [DCHN11] and\n[CS12]. Our result relies on new discrete complex analysis techniques,\nintroduced in [Che12]. We detail some applications, in particular the\ncomputation of so-called universal exponents, the proof of\nquasi-multiplicativity properties of arm probabilities, and bounds on crossing\nprobabilities for the classical Ising model.\n

Citations

• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition

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