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

TL;DR

This paper introduces a Monte Carlo importance-sampling method to accurately probe the extreme tails of ground-state energy distributions in disordered systems, validated on the Sherrington-Kirkpatrick model.

Contribution

The paper presents a novel, general importance-sampling algorithm that efficiently explores the tails of energy distributions using a guiding function derived from simple sampling.

Findings

Distribution fits a modified Gumbel distribution

Slope parameter m is larger than 6, around 11

Method achieves high-precision tail probing

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 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.