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

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

2005-06-29

arxiv.org/abs/cond-mat/0506780v3

Phys. Rev. B 72, 212408 (2005)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, RevTex, 1 eps-figure included, added derivation of Gumbel distribution in SK (for related articles see http://www.p

Scientific paper

10.1103/PhysRevB.72.212408

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.

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