Ground-state energy fluctuations in the Sherrington-Kirkpatrick model

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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≃ 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 ≃ 6.