Numerical Results for Spin Glass Ground States on Bethe Lattices: Gaussian Bonds

Abstract

The average ground state energies for spin glasses on Bethe lattices of connectivities r=3,...,15 are studied numerically for a Gaussian bond distribution. The Extremal Optimization heuristic is employed which provides high-quality approximations to ground states. The energies obtained from extrapolation to the thermodynamic limit smoothly approach the ground-state energy of the Sherrington-Kirkpatrick model for r->\infty. Consistently for all values of r in this study, finite-size corrections are found to decay approximately with ~N^{-4/5}. The possibility of ~N^{-2/3} corrections, found previously for Bethe lattices with a bimodal +-J bond distribution and also for the Sherrington-Kirkpatrick model, are constrained to the additional assumption of very specific higher-order terms. Instance-to-instance fluctuations in the ground state energy appear to be asymmetric up to the limit of the accuracy of our heuristic. The data analysis provides insights into the origin of trivial fluctuations when using continuous bonds and/or sparse networks.

RevTex4, 9 pages, 15 eps-figs included. More extensive analysis of finite-size corrections; final version. For related information, see http://www.physics.emory.edu/faculty/boettcher/

References in corpus (8)

• Finite size corrections in the Sherrington-Kirkpatrick model
• Universality in the level statistics of disordered systems
• Universality-class dependence of energy distributions in spin glasses
• Improved extremal optimization for the Ising spin glass
• Double Criticality of the Sherrington-Kirkpatrick Model at T=0
• Conjecture on the maximum cut and bisection width in random regular graphs
• Large Deviations of the Free-Energy in Diluted Mean-Field Spin-Glass
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• Simulations of Ground State Fluctuations in Mean-Field Ising Spin Glasses
• One-dimensional infinite component vector spin glass with long-range interactions
• Analysis of the Relation between Quadratic Unconstrained Binary Optimization (QUBO) and the Spin Glass Ground-State Problem
• Ground State Properties of the Diluted Sherrington-Kirkpatrick Spin Glass
• Ground States of the Sherrington-Kirkpatrick Spin Glass with Levy Bonds