Monte Carlo study of the universal area distribution of clusters in the honeycomb O(n) loop model

We investigate the area distribution of clusters (loops) in the honeycomb O(n) loop model by means of the worm algorithm with n = 0.5, 1, 1.5, and 2. At the critical point, the number of clusters, whose enclosed area is greater than A, is proportional to A−1 with a proportionality constant C. We confirm numerically that C is universal, and its value agrees well with the predictions based on the Coulomb gas method. (general)