Some Remarks on Hierarchical Replica Symmetry Breaking in Finite-Connectivity Systems


A functional formalism capable of handling the first step of Parisi's hierarchical symmetry breaking for finite--connectivity systems is introduced. The order parameter is proposed to be a probability distribution over the set of all cavity fields probability distributions inside each states. As an application, the ground state properties of the 2-Satisfiability model are investigated and some evidence for the occurence of replica symmetry breaking above the percolation threshold is exposed. I

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