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Updated: Jun 14, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Hierarchical random energy model of a spin glass
Michele Castellana1, Aurélien Decelle, Silvio Franz
1Laboratoire de Physique Théorique et Modèles Statistiques, CNRS - Université Paris Sud, Bâtiment 100, 91405 Orsay Cedex, France.
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.
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