Overlap Interfaces in Hierarchical Spin-Glass models

Abstract

We discuss interfaces in spin glasses. We present new theoretical results and a numerical method to characterize overlap interfaces and the stability of the spin-glass phase in extended disordered systems. We use this definition to characterize the low temperature phase of hierarchical spin-glass models. We use the Replica Symmetry Breaking theory to evaluate the cost for an overlap interface, which in these models is particularly simple. A comparison of our results from numerical simulations with the theoretical predictions shows good agreement.

References in corpus (7)

• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Probing the Almeida-Thouless line away from the mean-field model
• Stiffness of the Edwards-Anderson Model in all Dimensions
• Interfaces and Lower Critical Dimension in a Spin Glass Model
• Critical behaviour and ultrametricity of Ising spin-glass with long-range interactions
• Nonlinear Aspects of the Renormalization Group Flows of Dyson's Hierarchical Model
• Local Spin Glass Order in 1D

Cited by in corpus (25)

• Anderson localization transition and eigenfunction multifractality in ensemble of ultrametric random matrices
• The Hierarchical Random Energy Model
• Ensemble renormalization group for disordered systems
• Many-Body Localization : construction of the emergent local conserved operators via block real-space renormalization
• Real space Renormalization Group analysis of a non-mean field spin-glass
• Support for the value 5/2 for the spin glass lower critical dimension at zero magnetic field
• Non-perturbative effects in spin glasses
• 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
• Replica symmetry breaking, complexity and spin representation in the generalized random energy model
• Hierarchical spin glasses in a magnetic field: A renormalization-group study
• 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
• Spectral problem of block-rectangular hierarchical matrices
• 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
• New analysis of the free energy cost of interfaces in spin glasses
• Low-temperature dynamics of Long-Ranged Spin-Glasses : full hierarchy of relaxation times via real-space renormalization
• Cycle-expansion method for the Lyapunov exponent, susceptibility, and higher moments
• Real-space renormalization-group methods for hierarchical spin glasses
• Statistical mechanics of the spherical hierarchical model with random fields
• The Hierarchical Parity Model
• Order parameter for non-mean-field spin glasses