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

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.