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

We investigate the area distribution of clusters (loops) for the honeycomb O(n) loop model by means of 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.