Correlation Length From Cluster-Diameter Distribution

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 $1$. This is a considerable improvement over previous measurements using the standard (projected) two-point function.