Thermodynamic Identities and Symmetry Breaking in Short-Range Spin Glasses

Abstract

We present a technique to generate relations connecting pure state weights, overlaps, and correlation functions in short-range spin glasses. These are obtained directly from the unperturbed Hamiltonian and hold for general coupling distributions. All are satisfied in phases with simple thermodynamic structure, such as the droplet-scaling and chaotic pairs pictures. If instead nontrivial mixed-state pictures hold, the relations suggest that replica symmetry is broken as described by a Derrida-Ruelle cascade, with pure state weights distributed as a Poisson-Dirichlet process.

6 pages in main text plus a 3-page supplement

References in corpus (8)

• The critical behavior of three-dimensional Ising spin glass models
• The three dimensional Ising spin glass in an external magnetic field: the role of the silent majority
• Evidence of non-mean-field-like low-temperature behavior in the Edwards-Anderson spin-glass model
• Evidence against a mean field description of short-range spin glasses revealed through thermal boundary conditions
• Short-range Ising spin glasses: the metastate interpretation of replica symmetry breaking
• The cumulative overlap distribution function in realistic spin glasses
• Fluctuation Bounds For Interface Free Energies in Spin Glasses
• Explicit generation of the branching tree of states in spin glasses

Cited by in corpus (6)

• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• Numerical construction of the Aizenman-Wehr metastate
• Ground State Stability and the Nature of the Spin Glass Phase
• Proof of single-replica equivalence in short-range spin glasses
• Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman
• Deepening the knowledge of Spin Glasses: Metastate, Off-equilibrium phenomena and Temperature Chaos