Spatial Inhomogeneity and Thermodynamic Chaos

Abstract

We present a coherent approach to the competition between thermodynamic states in spatially inhomogeneous systems, such as the Edwards-Anderson spin glass with a fixed coupling realization. This approach explains and relates chaotic size dependence, ``dispersal of the metastate'', and for replicas: non-independence, symmetry breaking, and overlap (non-)self-averaging.

LaTeX file, 8 pages

References in corpus (3)

• Non-Mean-Field Behavior of Realistic Spin Glasses
• Interfaces and Lower Critical Dimension in a Spin Glass Model
• Replica Symmetry Breaking Instability in the 2D XY model in a random field

Cited by in corpus (50)

• Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences
• The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states
• Ordering and Broken Symmetry in Short-Ranged Spin Glasses
• The metastate approach to thermodynamic chaos
• Simplicity of State and Overlap Structure in Finite-Volume Realistic Spin Glasses
• Spin-Glass Stochastic Stability: a Rigorous Proof
• Numerical investigation of the thermodynamic limit for ground states in models with quenched disorder
• Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane
• Are There Incongruent Ground States in 2D Edwards-Anderson Spin Glasses?
• Metastable States in Spin Glasses and Disordered Ferromagnets
• Nature of Ground State Incongruence in Two-Dimensional Spin Glasses
• Short-range Ising spin glasses: the metastate interpretation of replica symmetry breaking
• Interfaces (and Regional Congruence?) in Spin Glasses
• Stochastic symmetry-breaking in a gaussian Hopfield model
• The influence of critical behavior on the spin glass phase
• One-step replica-symmetry-breaking phase below the de Almeida-Thouless line in low-dimensional spin glasses
• Number of thermodynamic states in the three-dimensional Edwards-Anderson spin glass
• Which measures of spin-glass overlaps are informative?
• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• The cumulative overlap distribution function in realistic spin glasses
• Finite-Dimensional Spin Glasses: States, Excitations, and Interfaces
• Low-temperature spin-glass behaviour in a diluted dipolar Ising system
• Non-equilibrium evolution of window overlaps in spin glasses
• Fluctuation Bounds For Interface Free Energies in Spin Glasses
• Numerical construction of the Aizenman-Wehr metastate
• Ground State Stability and the Nature of the Spin Glass Phase
• Factorization Properties in the 3D Edwards-Anderson Model
• Realistic spin glasses below eight dimensions: a highly disordered view
• Thermodynamic Identities and Symmetry Breaking in Short-Range Spin Glasses
• Proof of single-replica equivalence in short-range spin glasses
• Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: above and below the upper critical range
• (Non-) Gibbsianness and phase transitions in random lattice spin models
• Zero-Temperature Fluctuations in Short-Range Spin Glasses
• Metastates in the Hopfield model in the replica symmetric regime
• The weak limit of Ising models on locally tree-like graphs
• Numerical simulations of Ising spin glasses with free boundary conditions: the role of droplet excitations and domain walls
• Triviality of the ground-state metastate in long-range Ising spin glasses in one dimension
• Free Energy Difference Fluctuations in Short-Range Spin Glasses
• Infinite volume Gibbs states and metastates of the random field mean-field spherical model
• Overlap Structure and Free Energy Fluctuations in Short-Range Spin Glasses
• Critical Droplets and Replica Symmetry Breaking
• Response to Parisi's Comment on ``Non-mean-field behavior of realistic spin glasses''
• Local weak${}^{\ast }$-Convergence, algebraic actions, and a max-min principle
• Frustration and Fluctuations in Systems with Quenched Disorder
• Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman
• Strong random correlations in networks of heterogeneous agents
• Spherical Model in a Random Field
• Weakly Gibbsian representations for joint measures of quenched lattice spin models
• Ground State Incongruence In 2D Spin Glasses Revisited
• How non-Gibbsianness helps a metastable Morita minimizer to provide a stable free energy