Probing tails of energy distributions using importance-sampling in the disorder with a guiding function

We propose a simple and general procedure based on a recently introduced approach that uses an importance-sampling Monte Carlo algorithm in the disorder to probe to high precision the tails of ground-state energy distributions of disordered systems. Our approach requires an estimate of the ground-state energy distribution as a guiding function which can be obtained from simple-sampling simulations. In order to illustrate the algorithm, we compute the ground-state energy distribution of the Sherrington–Kirkpatrick mean-field Ising spin glass to 18 orders of magnitude. We find that if the ground-state energy distribution in the thermodynamic limit is described by a modified Gumbel distribution, as previously predicted, then the value of the slope parameter m is clearly larger than 6 and of the order of 11.

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