Exact Enumeration of Ground States in the Sherrington-Kirkpatrick Spin Glass

Abstract

Using the discrete $\pm J$ bond distribution for the Sherrington-Kirkpatrick spin glass, all ground states for the entire ensemble of the bond disorder are enumerated. Although the combinatorial complexity of the enumeration severely restricts attainable system sizes, here $N\le 9$, some remarkably intricate patterns found in previous studies already emerge. The analysis of the exact ground state frequencies suggests a direct construction of their probability density function. Against expectations, the result suggests that its highly skewed appearance for finite $N$ evolves logarithmically slow towards a Gaussian distribution.

arXiv comment4 pages, RevTex, 1 eps-figure included, added derivation of Gumbel distribution in SK (for related articles see http://www.physics.emory.edu/faculty/boettcher/publications.html)

References in corpus (6)

• Universality Classes for Extreme Value Statistics
• Optimization with Extremal Dynamics
• Energy exponents and corrections to scaling in Ising spin glasses
• Extremal Optimization for Sherrington-Kirkpatrick Spin Glasses
• Universality-class dependence of energy distributions in spin glasses
• Large deviations in spin-glass ground-state energies

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• Numerical Results for Spin Glass Ground States on Bethe Lattices: Gaussian Bonds
• Ground States of the Sherrington-Kirkpatrick Spin Glass with Levy Bonds
• Ground States of the Mean-Field Spin Glass with 3-Spin Couplings