Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences

Abstract

We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the problem of constructing pure states in spin glass systems. We mainly discuss what happens in finite-dimensional, realistic spin glasses. Together with a detailed review of some of the most important features, facts, data, and phenomena, we present some new theoretical ideas and numerical results. We discuss among others the basic idea of the RSB theory, correlation functions, interfaces, overlaps, pure states, random field, and the dynamical approach. We present new numerical results for the behaviors of coupled replicas and about the numerical verification of sum rules, and we review some of the available numerical results that we consider of larger importance (for example, the determination of the phase transition point, the correlation functions, the window overlaps, and the dynamical behavior of the system).

48 pages, 21 figures. v2: the published version

References in corpus (2)

• The response of glassy systems to random perturbations: A bridge between equilibrium and off-equilibrium
• About the overlap distribution in mean field spin glass models

Cited by in corpus (125)

• The effective temperature
• Critical Behavior of the Three-Dimensional Ising Spin Glass
• Nature of the Spin Glass State
• Monte Carlo Simulations of Spin Glasses at Low Temperatures
• Spin and link overlaps in 3-dimensional spin glasses
• Polynomial iterative algorithms for coloring and analyzing random graphs
• An in-depth view of the microscopic dynamics of Ising spin glasses at fixed temperature
• Ordering and Broken Symmetry in Short-Ranged Spin Glasses
• Nonequilibrium spin glass dynamics from picoseconds to 0.1 seconds
• Nature of the spin-glass phase at experimental length scales
• Quadratic replica coupling in the Sherrington-Kirkpatrick mean field spin glass model
• Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks
• The three dimensional Ising spin glass in an external magnetic field: the role of the silent majority
• Off-Equilibrium Dynamics at Very Low Temperatures in 3d Spin Glasses
• Aging rate of spin glasses from simulations matches experiments
• On the Effects of a Bulk Perturbation on the Ground State of 3D Ising Spin Glasses
• Spin Glass in a Field: a New Zero-Temperature Fixed Point in Finite Dimensions
• Interface energies in Ising spin glasses
• Static versus dynamic heterogeneities in the D = 3 Edwards-Anderson-Ising spin glass
• On the Effects of Changing the Boundary Conditions on the Ground State of Ising Spin Glasses
• Matching microscopic and macroscopic responses in glasses
• Topological Description of the Aging Dynamics in Simple Glasses
• Dynamical transition in the D = 3 Edwards-Anderson spin glass in an external magnetic field
• First steps of a nucleation theory in disordered systems
• Constructing explicit magnetic analogies for the dynamics of glass forming liquids
• Universality-class dependence of energy distributions in spin glasses
• Strong ergodicity breaking in aging of mean field spin glasses
• Hierarchical landscape of hard disk glasses
• Glassy dynamics near zero temperature
• A statics-dynamics equivalence through the fluctuation-dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements
• The Kac limit for finite-range spin glasses
• Corrections to Scaling are Large for Droplets in Two-Dimensional Spin Glasses
• Monte Carlo study of the spin-glass phase of the site-diluted dipolar Ising model
• Extended droplet theory for aging in short-ranged spin glasses and a numerical examination
• Ground states of two-dimensional $\pm$J Edwards-Anderson spin glasses
• Short-range Ising spin glasses: the metastate interpretation of replica symmetry breaking
• Testing statics-dynamics equivalence at the spin-glass transition in three dimensions
• On the Slowing Down of Spin Glass Correlation Length Growth:simulations meet experiments
• The Percolation Signature of the Spin Glass Transition
• Lack of Ultrametricity in the Low-Temperature phase of 3D Ising Spin Glasses
• Magnetic field chaos in the SK Model
• Spin glasses without time-reversal symmetry and the absence of a genuine structural glass transition
• Monte Carlo simulations of spin glasses at low temperatures: Effects of free boundary conditions
• Number of thermodynamic states in the three-dimensional Edwards-Anderson spin glass
• Non-compact local excitations in spin glasses
• Sample-to-sample fluctuations of the overlap distributions in the three-dimensional Edwards-Anderson spin glass
• Temperature chaos is a non-local effect
• Optimized GPU simulation of continuous-spin glass models
• Some considerations of finite dimensional spin glasses
• The marginally stable Bethe lattice spin glass revisited
• Jamming Energy Landscape is Hierarchical and Ultrametric
• Nature of the Spin-glass State in the Three-dimensional Gauge Glass
• On the structure of correlations in the three dimensional spin glasses
• Replica Cluster Variational Method: the Replica Symmetric solution for the 2D random bond Ising model
• Real Space Migdal-Kadanoff Renormalisation of Glassy Systems: Recent Results and a Critical Assessment
• Zero-temperature phase of the XY spin glass in two dimensions: Genetic embedded matching heuristic
• Numerical study of the SK Model in magnetic field
• Monte Carlo simulations of the four-dimensional XY spin glass at low temperatures
• Tethered Monte Carlo: Managing rugged free-energy landscapes with a Helmholtz-potential formalism
• Aging in Spin Glasses in three, four and infinite dimensions
• Discrete energy landscapes and replica symmetry breaking at zero temperature
• Absence of an equilibrium ferromagnetic spin glass phase in three dimensions
• Mean Field Spin Glass in the Observable Representation
• Non-equilibrium evolution of window overlaps in spin glasses
• Low-temperature spin-glass behaviour in a diluted dipolar Ising system
• The mean field theory of spin glasses: the heuristic replica approach and recent rigorous results
• Numerical construction of the Aizenman-Wehr metastate
• Low-temperature behavior of the statistics of the overlap distribution in Ising spin-glass models
• Zero temperature solutions of the Edwards-Anderson model in random Husimi Lattices
• A numerical study of the overlap probability distribution and its sample-to-sample fluctuations in a mean-field model
• Replica symmetric spin glass field theory
• Study of the phase transition in the 3d Ising spin glass from out of equilibrium numerical simulations
• Off-equilibrium fluctuation-dissipation relations in the 3d Ising Spin Glass in a magnetic field
• Magnetic Field Scaling in Spin Glasses and the Mean-Field Theory
• From Linear to Nonlinear Response in Spin Glasses: Importance of Mean-Field-Theory Predictions
• Statistics of lowest excitations in two dimensional Gaussian spin glasses
• Spin Glass Ordering in Diluted Magnetic Semiconductors: a Monte Carlo Study
• Absence of aging in the remanent magnetization in Migdal-Kadanoff spin glasses
• Statistics of lowest droplets in two-dimensional Gaussian Ising spin glasses
• Incoherent boundary conditions and metastates
• Spin Glasses on the Hypercube
• Local Spin Glass Order in 1D
• Ground State Stability and the Nature of the Spin Glass Phase
• Dynamics and energy landscape of the jammed spin-liquid
• Partition-function zeros of spherical spin glasses and their relevance to chaos
• Replica Symmetry Breaking without Replicas
• Thermodynamic Identities and Symmetry Breaking in Short-Range Spin Glasses
• Instability of the ferromagnetic phase under random fields in an Ising spin glass with correlated disorder
• Spin-glass dynamics: experiment, theory and simulation
• Factorization Properties in the 3D Edwards-Anderson Model
• Stable Mean Field Solution of a Short-Range Interacting SO(3) Quantum Heisenberg Spin-Glass
• Local overlaps, heterogeneities and the local fluctuation dissipation relations
• Realistic spin glasses below eight dimensions: a highly disordered view
• The connection between statics and dynamics of spin glasses
• A conjectured scenario for order-parameter fluctuations in spin glasses
• Order-parameter fluctuations in Ising spin glasses at low temperatures
• Equilibrium valleys in spin glasses at low temperature
• Spin Glass Theory: numerical and experimental results in three-dimensional systems
• Spin glasses in a field show a phase transition varying the distance among real replicas (and how to exploit it to find the critical line in a field)
• Quantum field theory solution for a short-range interacting SO(3) quantum spin-glass
• The Ising spin glass on random graphs at zero temperature: not all spins are glassy in the glassy phase
• A Quantitative Clustering Approach to Ultrametricity in Spin Glasses
• Spatial correlation functions and dynamical exponents in very large samples of 4D spin glasses
• Precursors of the Spin Glass Transition in Three Dimensions
• Evidence of many thermodynamic states of the three-dimensional Ising spin glass
• Low T Dynamical Properties of Spin Glasses Smoothly Extrapolate to T=0
• A simplified Parisi Ansatz
• Monte Carlo study of the two-dimensional site-diluted dipolar Ising model
• Spin-glass quantum phase transition in amorphous arrays of Rydberg atoms
• Numerical simulations of Ising spin glasses with free boundary conditions: the role of droplet excitations and domain walls
• Zero-temperature Monte Carlo simulations of two-dimensional quantum spin glasses guided by neural network states
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• Uniqueness of ground state in the Edwards-Anderson spin glass model
• The Eigenvalue Analysis of the Density Matrix of 4D Spin Glasses Supports Replica Symmetry Breaking
• Slow Spin Dynamics and Self-Sustained Clusters in Sparsely Connected Systems
• The Effect of Pure State Structure on Nonequilibrium Dynamics
• Free Energy Difference Fluctuations in Short-Range Spin Glasses
• Critical Droplets and Replica Symmetry Breaking
• Correlated Domains in Spin Glasses
• Cluster structure of optimal solutions in bipartitioning of small worlds
• Bipartitioning of directed and mixed random graphs
• The Most Dispersed Subset of Random Points in ${\mathbb{R}}^d$
• Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman
• Exact mapping of a spin glass with correlated disorder to the pure Ising model
• Deepening the knowledge of Spin Glasses: Metastate, Off-equilibrium phenomena and Temperature Chaos