Monte Carlo study of cluster-diameter distribution: An observable to estimate correlation lengths

We report numerical simulations of two-dimensional q-state Potts models with emphasis on a new quantity for the computation of spatial correlation lengths. This quantity is the cluster-diameter distribution function G(x), which measures the distribution of the diameter of stochastically defined cluster. Theoretically it is predicted to fall off exponentially for large diameter x , G}exp(2x/j), where j is the correlation length as usually defined through the large-distance behavior of two-point correlation functions. The results of our extensive Monte Carlo study in the disordered phase of the models with q510, 15, and 20 on large square lattices of size 3003300, 1203120, and 80380, respectively, clearly confirm the theoretically predicted behavior. Moreover, using this observable we are able to verify an exact formula for the correlation length jd(b t) in the disordered phase at the first-order transition point b t with an accuracy of about 1% –2% for all considered values of q . This is a considerable improvement over estimates derived from the large-distance behavior of standard ~projected! two-point correlation functions, which are also discussed for comparison. @S1063-651X~97!11907-9#