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

2006/03/31 by Mathias Koerner, Mathias Körner, Helmut G. Katzgraber +1 · 3 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Theoretical and Computational Physics #cond-mat.dis-nn

paper · pdf · doi:10.1088/1742-5468/2006/04/p04005

published as J. Stat. Mech. P04005 (2006) · 7 pages, 5 figures, 3 tables

arxiv created 2006/04/26 · openalex publication_date 2006/04/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

Abstract

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.

Citations

• A Guide to Monte Carlo Simulations in Statistical Physics

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