In this Letter we address the nature of broken ergodicity in the low temperature phase of Ising spin glasses by examining spectral properties of spin correlation functions $C_{\mathrm{ij}}\equiv 〈S_i{S}_j〉$. We argue that more than one extensive [i.e., $O\left(N\right)$] 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.

• Received 24 May 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.2609