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

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dc.creatorBoettcher, Stefan
dc.creatorKott, Tomasz M.
dc.date2005-06-29
dc.date2005-08-21
dc.date.accessioned2026-07-07T06:25:20Z
dc.date.available2026-07-07T06:25:20Z
dc.descriptionUsing 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 $N\leq9$, 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.
dc.description4 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)
dc.identifierhttps://arxiv.org/abs/cond-mat/0506780
dc.identifierhttp://arxiv.org/abs/cond-mat/0506780
dc.identifierPhys. Rev. B 72, 212408 (2005)
dc.identifierdoi:10.1103/PhysRevB.72.212408
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96803
dc.subjectDisordered Systems and Neural Networks
dc.subjectStatistical Mechanics
dc.titleExact Enumeration of Ground States in the Sherrington-Kirkpatrick Spin Glass
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