The nature of ergodicity breaking in Ising spin glasses as revealed by correlation function spectral properties

Abstract

In this work we address the nature of broken ergodicity in the low temperature phase of Ising spin glasses by examining spectral properties of spin correlation functions $C_{ij}\equiv <S_i{S}_j>$. We argue that more than one extensive (i.e., O(N)) eigenvalue in this matrix signals replica symmetry breaking. Monte-Carlo simulations of the infinite-range Ising spin-glass model, above and below the Almeida-Thouless line, support this conclusion. Exchange Monte-Carlo simulations for the short-range model in four dimensions find a single extensive eigenvalue and a large subdominant eigenvalue consistent with droplet model expectations.

4 pages, 3 figures, accepted for publication in Phys. Rev. Lett

References in corpus (4)

• Chiral-glass transition and replica symmetry breaking of a three-dimensional Heisenberg spin glass
• Triviality of the Ground State Structure in Ising Spin Glasses
• Calculation of ground states of four-dimensional +or- J Ising spin glasses
• Numerical Simulations of the 4D Edwards-Anderson Spin Glass with Binary Couplings

Cited by in corpus (10)

• Universality-class dependence of energy distributions in spin glasses
• High-Dimensional Inference with the generalized Hopfield Model: Principal Component Analysis and Corrections
• Monte Carlo study of the spin-glass phase of the site-diluted dipolar Ising model
• The Quantum Transition of the Two-Dimensional Ising Spin Glass: A Tale of Two Gaps
• Clustering analysis of the ground-state structure of the vertex-cover problem
• Extensive eigenvalues in spin-spin correlations: a tool for counting pure states in Ising spin glasses
• Solution-space structure of (some) optimization problems
• Nature and number of distinct phases in the random field Ising model
• Large random correlations in individual mean field spin glass samples
• The Eigenvalue Analysis of the Density Matrix of 4D Spin Glasses Supports Replica Symmetry Breaking