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

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

2000-07-31

arxiv.org/abs/cond-mat/0007509v1

Phys. Rev. Lett. 85, 2609 (2000)

Physics

Condensed Matter

Disordered Systems and Neural Networks

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

Scientific paper

10.1103/PhysRevLett.85.2609

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.

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