Phase transition in an optimal clusterization model

An optimal clusterization model resembling the infinite-range Potts glass-type model with ±J±J bonds and unrestricted number of states, p=Np=N is introduced and studied. As a function of the q   probability of +J+J bonds, it is found that the r   relative size of the largest cluster, or, coalition, shows a percolation-like transition at q=12. By a simple renormalization approach and several optimization methods we investigate the r(q)r(q) curves for finite system sizes. Non-trivial consequences for social percolation problems are discussed.