2009/12/31 by Michele Castellana, Aurélien Decelle, Aurelien Decelle +4 · 3 citations
Economics, Econometrics and Finance · Materials Science · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Computer science #Condensed matter physics #Geology #Hierarchical database model #Lattice (music) #Lattice model (finance) #Material Dynamics and Properties #Materials science #Mathematics #Mean field theory #Nuclear magnetic resonance #Physics #Polymer #Quantum mechanics #Random field #Series (stratigraphy) #Series expansion #Spin glass #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.104.127206
published as Physical Review Letters 104(12), 127206 (2010)
arxiv created 2010/03/02 · openalex publication_date 2010/03/26 · arxiv updated 2014/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.