  A scheme to provide various mean-field-type approximation algorithms is
presented by employing the Bethe free energy formalism to a family of
replicated systems in conjunction with analytical continuation with respect to
the number of replicas. In the scheme, survey propagation (SP), which is an
efficient algorithm developed recently for analyzing the microscopic properties
of glassy states for a fixed sample of disordered systems, can be reproduced by
assuming the simplest replica symmetry on stationary points of the replicated
Bethe free energy. Belief propagation and generalized SP can also be offered in
the identical framework under assumptions of the highest and broken replica
symmetries, respectively.
