Ground-state energy fluctuations in the Sherrington-Kirkpatrick model

Abstract

The probability distribution function (PDF) of the ground-state energy in the Sherrington-Kirkpatrick spin-glass model is numerically determined by collecting a large statistical sample of ground states, computed using a genetic algorithm. It is shown that the standard deviation of the ground-state energy per spin scales with the number of spins, N, as N^{-ρ} with ρ\simeq 0.765, but the value ρ=3/4 is also compatible with the data, while the previously proposed value ρ=5/6 is ruled out. The PDF satisfies finite-size scaling with a non-Gaussian asymptotic PDF, which can be fitted remarkably well by the Gumbel distribution for the m-th smallest element in a set of random variables, with m \simeq 6.