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We present and solve the Replica Symmetric equations in the context of theReplica Cluster Variational Method for the 2D random bond Ising model(including the 2D Edwards-Anderson spin glass model). First we solve alinearized version of these equations to obtain the phase diagrams of the modelon the square and triangular lattices. In both cases the spin-glass transitiontemperatures and the tricritical point estimations improve largely over theBethe predictions. Moreover, we show that this phase diagram is consistent withthe behavior of inference algorithms on single instances of the problem.Finally, we present a method to consistently find approximate solutions to theequations in the glassy phase. The method is applied to the triangular latticedown to T=0, also in the presence of an external field.

Replica Cluster Variational Method: the Replica Symmetric solution for the 2D random bond Ising model