• Corpus ID: 115175836

Connection probabilities and RSW-type bounds for the FK Ising model

  title={Connection probabilities and RSW-type bounds for the FK Ising model},
  author={Hugo Duminil-Copin and Cl{\'e}ment Hongler and Pierre Nolin},
  journal={arXiv: Probability},
We prove Russo-Seymour-Welsh-type uniform bounds on crossing probabilities for the FK Ising model at criticality, independent of the boundary conditions. Our proof relies mainly on Smirnov's fermionic observable for the FK Ising model, which allows us to get precise estimates on boundary connection probabilities. It remains purely discrete, in particular we do not make use of any continuum limit, and it can be used to derive directly several noteworthy results - some new and some not - among… 

Convergence of Fermionic Observables in the Massive Planar FK-Ising Model

  • S. C. Park
  • Mathematics
    Communications in Mathematical Physics
  • 2022
We prove convergence of the 2- and 4-point fermionic observables of the FK-Ising model on simply connected domains discretised by a planar isoradial lattice in massive (near-critical) scaling limit.

Smirnov's fermionic observable away from criticality

In a recent and celebrated article, Smirnov [Ann. of Math. (2) 172 (2010) 1435–1467] defines an observable for the self-dual random-cluster model with cluster weight q=2 on the square lattice Z2, and

Conformal Invariance of Spin Pattern Probabilities in the Planar Ising Model

We study the 2-dimensional Ising model at critical temperature on a smooth simply-connected graph Ω.We rigorously prove the conformal invariance of arbitrary spin-pattern probabilities centered at a

Polychromatic Arm Exponents for the Critical Planar FK-Ising Model

Schramm–Loewner evolution (SLE) is a one-parameter family of random planar curves introduced by Schramm in 1999 as the candidates for the scaling limits of the interfaces in the planar critical

Renormalization of crossing probabilities in the dilute Potts model

A recent paper due to Duminil-Copin and Tassion from 2019 introduces a novel argument for obtaining estimates on horizontal crossing probabilities of the random cluster model, in which a range of

Critical Ising on the Square Lattice Mixes in Polynomial Time

The Ising model is widely regarded as the most studied model of spin-systems in statistical physics. The focus of this paper is its dynamic (stochastic) version, the Glauber dynamics, introduced in

The critical temperature of the Ising model on the square lattice, an easy way

AbstractThe goal of this article is twofold. First, we present a short derivation of the critical tem-perature for the Ising model on the square lattice, using recent techniques developed for

Ising interfaces and free boundary conditions

The authors generalize the result of D. Chelkak et al. [C. R., Math., Acad. Sci. Paris 352, No. 2, 157{161 (2014; Zbl 06265643)] to the case when free boundary conditions enter the picture. The proof

Conformal Invariance of Ising Model Correlations

We review recent results with D. Chelkak and K. Izyurov, where we rigorously prove existence and conformal invariance of scaling limits of magnetization and multi-point spin correlations in the

Planar Ising magnetization field I. Uniqueness of the critical scaling limit

The aim of this paper is to prove the following result. Consider the critical Ising model on the rescaled grid $a\mathbb{Z}^2$, then the renormalized magnetization field \[\Phi^a:=a^{15/8}\sum_{x\in



Universality in the 2D Ising model and conformal invariance of fermionic observables

It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no

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The partition function of a two-dimensional "ferromagnetic" with scalar "spins" (Ising model) is computed rigorously for the case of vanishing field. The eigenwert problem involved in the

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