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

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

2006-03-10

arxiv.org/abs/cond-mat/0603290v2

J. Stat. Mech. P04005 (2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages, 5 figures, 3 tables

Scientific paper

10.1088/1742-5468/2006/04/P04005

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 eighteen orders of magnitude. We find that the ground-state energy distribution in the thermodynamic limit is well fitted by a modified Gumbel distribution as previously predicted, but with a value of the slope parameter m which is clearly larger than 6 and of the order 11.

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