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.

4 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 (1)

• Universality-class dependence of energy distributions in spin glasses

Cited by in corpus (5)

• Universality-class dependence of energy distributions in spin glasses
• Probing the tails of the ground state energy distribution for the directed polymer in a random medium of dimension $d=1,2,3$ via a Monte-Carlo procedure in the disorder
• Probing tails of energy distributions using importance-sampling in the disorder with a guiding function
• Spin glasses and algorithm benchmarks: A one-dimensional view
• Ground States of the Mean-Field Spin Glass with 3-Spin Couplings