Griffiths singularities in the two dimensional diluted Ising model

TL;DR

This paper numerically investigates the distribution of Yang-Lee zeros in the Griffiths phase of a 2D diluted Ising model, confirming analytical predictions and extracting the anomalous dimension at phase transitions.

Contribution

It provides numerical validation of the shape of the Yang-Lee zero distribution and estimates the anomalous dimension for specific dilutions in the 2D diluted Ising model.

Findings

Distribution shape matches analytical predictions

Anomalous dimension η agrees with previous estimates

Finite size scaling analysis is effective for phase transition study

Abstract

We study numerically the probability distribution of the Yang-Lee zeroes inside the Griffiths phase for the two dimensional site diluted Ising model and we check that the shape of this distribution is that predicted in previous analytical works. By studying the finite size scaling of the averaged smallest zero at the phase transition we extract, for two values of the dilution, the anomalous dimension, $\eta$, which agrees very well with the previous estimated values.