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Smirnov's fermionic observable away from criticality 

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Published in  Annals of Probability. 2012, vol. 40, no. 6, p. 26672689  
Abstract  In a recent and celebrated article, Smirnov [Ann. of Math. (2) 172 (2010) 14351467] defines an observable for the selfdual randomcluster model with cluster weight q = 2 on the square lattice $mathbb{Z}^2$, and uses it to obtain conformal invariance in the scaling limit. We study this observable away from the selfdual point. From this, we obtain a new derivation of the fact that the selfdual and critical points coincide, which implies that the critical inverse temperature of the Ising model equals $1/2log(1+sqrt{2})$. 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 2dIsing model (2006) Preprint]), which allows us to compute it explicitly.  
Identifiers  DOI: 10.1214/11AOP689 arXiv: 1010.0526  
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Citation (ISO format)  BEFFARA, Vincent, DUMINILCOPIN, Hugo. Smirnov's fermionic observable away from criticality. In: Annals of Probability, 2012, vol. 40, n° 6, p. 26672689. https://archiveouverte.unige.ch/unige:30545 