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

Stefan Boettcher; Tomasz M. Kott

doi:10.1103/physrevb.72.212408

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

Stefan Boettcher·Tomasz M. Kott

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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 $N\leq9$, 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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Stefan Boettcher, Tomasz M. Kott. 2005-08-21. Exact Enumeration of Ground States in the Sherrington-Kirkpatrick Spin Glass. https://doi.org/10.1103/physrevb.72.212408

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