Sample-to-sample fluctuations of the overlap distributions in the three-dimensional Edwards-Anderson spin glass

Abstract

We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, Stochastic Stability and Overlap Equivalence impose constraints on the moments of the overlap probability densities that can be tested against numerical data. We found small deviations from the Ghirlanda-Guerra predictions, which get smaller as system size increases. We also focus on the shape of the overlap distribution, comparing the numerical data to a mean-field-like prediction in which finite-size effects are taken into account by substituting delta functions with broad peaks

11 pages, 8 figures; version accepted for publication on PRB and updated Refs

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• Reconfigurable computing for Monte Carlo simulations: results and prospects of the Janus project
• Comment on "Evidence of Non-Mean-Field-Like Low-Temperature Behavior in the Edwards-Anderson Spin-Glass Model"
• The cumulative overlap distribution function in realistic spin glasses
• Low-temperature spin-glass behaviour in a diluted dipolar Ising system
• Numerical construction of the Aizenman-Wehr metastate
• Message passing and Monte Carlo algorithms: connecting fixed points with metastable states
• Spin-glass dynamics: experiment, theory and simulation
• Explicit generation of the branching tree of states in spin glasses
• Pair correlation function for spin glasses
• Analytical solution to Heisenberg spin glass models on sparse random graphs and their de Almeida-Thouless line