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

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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 $N\leq9$, 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.
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)

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Disordered Systems and Neural Networks, Statistical Mechanics

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http://salesiana.dossiersoluciones.com/handle/123456789/96803

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cond-mat/0506780
 http://arxiv.org/abs/cond-mat/0506780
 Phys. Rev. B 72, 212408 (2005)
 doi:10.1103/PhysRevB.72.212408

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arXiv