Hierarchical random energy model of a spin glass.
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.
Castellana
Michele
M
Laboratoire de Physique Théorique et Modèles Statistiques, CNRS - Université Paris Sud, Bâtiment 100, 91405 Orsay Cedex, France.
Decelle
Aurélien
A
Franz
Silvio
S
Mézard
Marc
M
Parisi
Giorgio
G