The Hierarchical Random Energy Model

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 occuring in the usual mean field Random Energy Model. At variance with mean field, the high temperature branch of the free-energy is non-analytic at the transition point.

References in corpus (3)

• Spin-Glass Theory for Pedestrians
• Overlap Interfaces in Hierarchical Spin-Glass models
• Exact Analytic Continuation with Respect to the Replica Number in the Discrete Random Energy Model of Finite System Size

Cited by in corpus (35)

• Theoretical perspective on the glass transition and amorphous materials
• Perspective: The Glass Transition
• Exact theory of dense amorphous hard spheres in high dimension. III. The full RSB solution
• Microscopic theory of the jamming transition of harmonic spheres
• A microscopic mean-field theory of the jamming transition
• From Dyson to Hopfield: Processing on hierarchical networks
• Renormalization group analysis of the random first order transition
• Quantitative approximation schemes for glasses
• Many-Body Localization : construction of the emergent local conserved operators via block real-space renormalization
• Hierarchical neural networks perform both serial and parallel processing
• Random Field Ising-like effective theory of the glass transition II: Finite Dimensional Models
• Real Space Renormalization Group Theory of Disordered Models of Glasses
• Random-Field Ising like effective theory of the glass transition: I Mean-Field Models
• A critical Dyson hierarchical model for the Anderson localization transition
• Meta-stable states in the hierarchical Dyson model drive parallel processing in the hierarchical Hopfield network
• First-passage phenomena in hierarchical networks
• Replica symmetry breaking, complexity and spin representation in the generalized random energy model
• Dyson Hierarchical Long-Ranged Quantum Spin-Glass via real-space renormalization
• Random field Ising model : statistical properties of low-energy excitations and of equilibrium avalanches
• Ensemble renormalization group for the random field hierarchical model
• Topological properties of hierarchical networks
• One-dimensional Ising spin-glass with power-law interaction : real-space renormalization at zero temperature
• Low Temperature Domain Wall Freezing and Non-Equilibrium Dynamics in the Transverse-Field Ising Model Material CoNb${}_2$O${}_6$
• Dyson hierarchical quantum ferromagnetic Ising chain with pure or random transverse fields
• Critical Exponents of the Random Field Hierarchical Model
• Dynamical Barriers in the Dyson Hierarchical model via Real Space Renormalization
• Extreme-Value Distributions and the Freezing Transition of Structural Glasses
• A walk in the statistical mechanical formulation of neural networks
• Theory of simple glasses
• Low-temperature dynamics of Long-Ranged Spin-Glasses : full hierarchy of relaxation times via real-space renormalization
• Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder
• Rigorous Results for Hierarchical Models of Structural Glasses
• Statistical mechanics of the spherical hierarchical model with random fields
• The Hierarchical Parity Model
• Disordered statistical physics in low dimensions: extremes, glass transition, and localization