Replica Cluster Variational Method |
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Authors: | Tommaso Rizzo Alejandro Lage-Castellanos Roberto Mulet and Federico Ricci-Tersenghi |
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Institution: | 1.“E. Fermi” Center,Rome,Italy;2.“Henri-Poincaré-Group” of Complex Systems and Department of Theoretical Physics, Physics Faculty,University of Havana,La Habana,Cuba;3.Dipartimento di Fisica, INFN Sezione di Roma1 and CNR-INFM,Sapienza Università di Roma,Rome,Italy |
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Abstract: | We present a general formalism to make the Replica-Symmetric and Replica-Symmetry-Breaking ansatz in the context of Kikuchi’s
Cluster Variational Method (CVM). Using replicas and the message-passing formulation of CVM we obtain a variational expression
of the replicated free energy of a system with quenched disorder, both averaged and on a single sample, and make the hierarchical
ansatz using functionals of functions of fields to represent the messages. We obtain a set of integral equations for the message
functionals. The main difference with the Bethe case is that the functionals appear in the equations in implicit form and
are not positive definite, thus standard iterative population dynamic algorithms cannot be used to determine them. In the
simplest cases the solution could be obtained iteratively using Fourier transforms. |
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