Monte Carlo Simulation on the Phase Transition of Animal Group

Abstract

In this work, we proposed a new model in order to study the phase transition behaviour of animal group. The individuals in the group are considered as the XY spins which can move freely in a plane with the same speed. For the interactions between every pairs of the individuals, we used the Hamiltonian of the system in the model of spin current with including a long-range Morse potential. Using the Monte-Carlo simulation technique, we obtained the main parameters of the model: the averaged velocity of all individuals which is equivalent to the order parameter or magnetization for the spin model, and the concentration of the individuals. The simulation result clearly shows that the system has three phases which correspond to the uncollected, flocking (schooling) and runaway behaviors at very low, medium and high noise, respectively. The simulation predictions are in good agreement with experimental observations.