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

• Main Authors: Boettcher, Stefan, Kott, Tomasz M
• Format: Journal Article
• Language: English
• Published: 29-06-2005
• Subjects: Physics - Disordered Systems and Neural Networks; Physics - Statistical Mechanics
• DOI: 10.48550/arxiv.cond-mat/0506780

Phys. Rev. B 72, 212408 (2005) 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.