Conformal invariance of spin correlations in the planar Ising model

By Dmitry Chelkak, Clément Hongler, K. Izyurov. 2012

187 citations recorded by the source corpus.

We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of conjectures coming from the physical and the mathematical literature. The proof relies on convergence results for discrete holomorphic spinor observables and probabilistic techniques.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8cbe01096e1fc8c43b1be39807ed2fc820cbd2f1

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In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Toeplitz Matrices and Toeplitz Determinants under the Impetus of the Ising Model: Some History and Some Recent Results (2012, methodology): “een (106) and (114). Recently two additional independent proofs of the rotational symmetry of hσ1,1 σ1+ℓ,1+mi as k= √ ℓ2 +m2 → ∞ have been given by Dub´edat [Dub] and by Chelkak, Hongler, and Izyurov [CheHonIzy]. In [Dub] the author proceeds by equating the product of two Ising correlators with a fr”
Convergence of Ising interfaces to Schramm's SLE curves (2013, background): “This paved a way to an ongoing project of rigorously establishing conformally covariant scaling limits for all critical Ising correlation functions, [11, 10, 4, 7].”
Conformal invariance in the long-range Ising model (2015, background): “Smirnov for nonlocal observables such as interfaces [44], and recently extended to correlation functions of local operators in bounded domains [45].”