  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 $\mathbb{Z}^2$, 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 $1/2\log(1+\sqrt{2})$.
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 2d-Ising model (2006)
Preprint]), which allows us to compute it explicitly.
