title: Hierarchical random energy model of a spin glass.
abstract: We introduce a random energy model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a non-mean-field model. Through small coupling series expansion and a direct numerical solution of the model, we provide evidence for a spin-glass condensation transition similar to the one occurring in the usual mean-field random energy model. At variance with the mean field, the high temperature branch of the free-energy is nonanalytic at the transition point.
authors.affiliation: Laboratoire de Physique Théorique et Modèles Statistiques, CNRS - Université Paris Sud, Bâtiment 100, 91405 Orsay Cedex, France.
authors.forename: Michele
authors.initials: M
authors.lastname: Castellana
authors.forename: Aurélien
authors.initials: A
authors.lastname: Decelle
authors.forename: Silvio
authors.initials: S
authors.lastname: Franz
authors.forename: Marc
authors.initials: M
authors.lastname: Mézard
authors.forename: Giorgio
authors.initials: G
authors.lastname: Parisi