Phase transition in an optimal clusterization model

Z. Neda, R. Florian, M. Ravasz, A. Libal, and G. Gyorgyi

An optimal clusterization model resembling the infinite-range Potts glass-type model with +/- J bonds and unrestricted number of states, p=N is introduced and studied. As a function of the q probability of +J bonds, it is found that the r relative size of the largest cluster or coalition shows a percolation-like transition at q =1/2. By a simple renormalization approach and several optimization methods we investigate the r(q) curves for finite system sizes. Non-trivial consequences for social percolation problems are discussed.