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We consider the large order behavior of the perturbative expansion of the scalar φ4 field theory in terms of a perturbative expansion around an instanton solution. We have computed the series of the free energy up to two-loop order in two and three dimension. Topologically there is only an additional Feynman diagram with respect to the previously known one dimensional case, but a careful treatment...
Physicists understand mean-field spin-glass models as possessing a complex free-energy landscape with many equilibrium states. The problem of chaos concerns the evolution of this landscape upon changing the external parameters of the system and is considered relevant for the interpretation of important features of real spin-glass and for understanding the performance of numerical algorithms. The subject...
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...
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