The evolution of cooperative behaviour is studied in the deterministic version of the Prisoners’ Dilemma on a two-dimensional lattice. The payoff parameter is set at the critical region 1.8 < b < 2.0 , where clusters of cooperators are formed in all spatial sizes. Using the factorial moments developed in particle and nuclear physics for the study of phase transition, the distribution of coopera...

A matrix model to describe dynamical loops on random planar graphs is analyzed. It has similarities with a model studied by Kazakov, few years ago, and the O(n) model by Kostov and collaborators. The main diierence is that all loops are coherently oriented and empty. The free energy is analytically evaluated and the two critical phases are analyzed, where the free energy exhibits the same criti...

We study the state behaviour of self-propelled and Brownian squares as a function of the magnitude of self-propulsion and density using Brownian dynamics simulations. We find that the system undergoes a transition from a fluid state to phase coexistence with increased self-propulsion and density. Close to the transition we find oscillations of the system between a fluid state and phase coexiste...