  Mean field-like approximations (including naive mean field, Bethe and Kikuchi
and more general Cluster Variational Methods) are known to stabilize ordered
phases at temperatures higher than the thermodynamical transition. For example,
in the Edwards-Anderson model in 2-dimensions these approximations predict a
spin glass transition at finite $T$. Here we show that the spin glass solutions
of the Cluster Variational Method (CVM) at plaquette level do describe well
actual metastable states of the system. Moreover, we prove that these states
can be used to predict non trivial statistical quantities, like the
distribution of the overlap between two replicas. Our results support the idea
that message passing algorithms can be helpful to accelerate Monte Carlo
simulations in finite dimensional systems.
