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A scheme to provide various mean-field-type approximation algorithms ispresented by employing the Bethe free energy formalism to a family ofreplicated systems in conjunction with analytical continuation with respect tothe number of replicas. In the scheme, survey propagation (SP), which is anefficient algorithm developed recently for analyzing the microscopic propertiesof glassy states for a fixed sample of disordered systems, can be reproduced byassuming the simplest replica symmetry on stationary points of the replicatedBethe free energy. Belief propagation and generalized SP can also be offered inthe identical framework under assumptions of the highest and broken replicasymmetries, respectively.Comment: appeared in Journal of the Physical Society of Japan 74, 2133-2136  (2005

Replicated Bethe Free Energy: A Variational Principle behind Survey Propagation