2000/10/19 by Jairo Sinova, Geoff Canright, Horacio E. Castillo +2 · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Condensed matter physics #Correlation function (quantum field theory) #Eigenvalues and eigenvectors #Ergodicity #Ising model #Physics #Quantum mechanics #Replica #Spin (aerodynamics) #Spin glass #Statistical physics #Symmetry breaking #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.63.104427
published as Phys. Rev. B 63, 104427 (2001) · 14 pages, 7 figures, submitted to PRB
arxiv created 2000/10/19 · openalex publication_date 2001/02/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the nature of the broken ergodicity in the low temperature phase of Ising spin glass systems, using as a diagnostic tool the spectrum of eigenvalues of the spin-spin correlation function. We show that multiple extensive eigenvalues of the correlation matrix Cij\ensuremath≡〈SiSj〉 occur if and only if there is replica symmetry breaking. We support our arguments with Exchange Monte Carlo results for the infinite-range problem. Here we find multiple extensive eigenvalues in the replica symmetry breaking (RSB) phase for N\ensuremath\gtrsim200, but only a single extensive eigenvalue for phases with long-range order but no RSB. Numerical results for the short-range model in four spatial dimensions, for N<~1296, are consistent with the presence of a single extensive eigenvalue, with the subdominant eigenvalue behaving in agreement with expectations derived from the droplet model. Because of the small system sizes we cannot exclude the possibility of replica symmetry breaking with finite size corrections in this regime.