Correlation Length From Cluster-Diameter Distribution

TL;DR

This paper introduces a numerical method to estimate correlation lengths in 2D Potts models using cluster-diameter distribution decay, achieving high accuracy and verifying theoretical predictions at phase transition points.

Contribution

It presents a novel approach to measure correlation lengths via cluster-diameter distribution decay, improving accuracy over traditional two-point function methods.

Findings

Verified theoretical correlation length predictions at q=10, 15, 20 with 1-2% accuracy.

Demonstrated the effectiveness of the cluster-diameter distribution method.

Achieved significant improvement over previous measurement techniques.

Abstract

We report numerical estimates of correlation lengths in 2D Potts models from the asymptotic decay of the cluster-diameter distribution. Using this observable we are able to verify theoretical predictions for the correlation length in the disordered phase at the transition point for $q=10$, 15, and 20 with an accuracy of about $1%-2%$. This is a considerable improvement over previous measurements using the standard (projected) two-point function.