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Hierarchical Random Energy Model of a Spin Glass

2010; American Physical Society; Volume: 104; Issue: 12 Linguagem: Inglês

10.1103/physrevlett.104.127206

1092-0145

Michele Castellana, Aurélien Decelle, Silvio Franz, Marc Mézard, Giorgio Parisi,

Complex Systems and Time Series Analysis

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.