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.
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