Smirnov's fermionic observable away from criticality

Abstract : 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 uses it to obtain conformal invariance in the scaling limit. We study this observable away from the self-dual point. From this, we obtain a new derivation of the fact that the self-dual and critical points coincide, which implies that the critical inverse temperature of the Ising model equals 12 log(1 + √ 2). Moreover, we relate the correlation length of the model to the large deviation behavior of a certain massive random walk (thus confirming an observation by Messikh [The surface tension near criticality of the 2d-Ising model (2006) Preprint]), which allows us to compute it explicitly.
Complete list of metadatas

Cited literature [2 references]  Display  Hide  Download

https://hal-ens-lyon.archives-ouvertes.fr/ensl-00523497
Contributor : Vincent Beffara <>
Submitted on : Thursday, January 25, 2018 - 6:39:41 PM
Last modification on : Friday, January 26, 2018 - 2:18:06 PM
Long-term archiving on : Thursday, May 24, 2018 - 6:46:36 PM

File

BD:ising.pdf
Publisher files allowed on an open archive

Identifiers

Collections

Citation

Vincent Beffara, Hugo Duminil-Copin. Smirnov's fermionic observable away from criticality . Annals of Probability, Institute of Mathematical Statistics, 2012, 40 (6), pp.2667 - 2689. ⟨10.1214/11-AOP689⟩. ⟨ensl-00523497⟩

Share

Metrics

Record views

124

Files downloads

109