A Monte Carlo Algorithm for Sampling Rare Events: Application to a Search for the Griffiths Singularity

TL;DR

This paper introduces an importance-sampling Monte Carlo method to efficiently sample rare events in disordered systems, applied specifically to study the Griffiths singularity in a 2D bond-diluted Ising model, revealing exponential tails in susceptibility distribution.

Contribution

The paper develops and applies a novel Monte Carlo importance-sampling algorithm to analyze rare events and Griffiths singularity in disordered systems.

Findings

Distribution of inverse susceptibility has an exponential tail.

Griffiths singularity linked to rare large clusters.

Method effectively samples rare events in disordered systems.

Abstract

We develop a recently proposed importance-sampling Monte Carlo algorithm for sampling rare events and quenched variables in random disordered systems. We apply it to a two dimensional bond-diluted Ising model and study the Griffiths singularity which is considered to be due to the existence of rare large clusters. It is found that the distribution of the inverse susceptibility has an exponential tail down to the origin which is considered the consequence of the Griffiths singularity.