Exact enumeration of ground states in the Sherrington-Kirkpatrick spin glass

Using the discrete ±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≤9 , 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 indicates that its highly skewed appearance for finite N evolves logarithmically slow towards a Gaussian distribution.