Study on the Phase Transition Behavior of Fishes Schooling System

Abstract

The Vicsek’s model (VM) [T. Vicsek, et. al., Phys. Rev. Lett. 75, 1226 (1995)] is apopular approach to study nature of the phase transition of self-propelling system. In this model,the direction of motion of each particle depends on the average velocity of its neighboring particleswithin a circle of radius R. In this work, we consider a group of fishes as the particles, but weassumed that only the individuals of its neighbors within a circle sector with central angle ϕ (iscalled angle of view) and radius R, are taken into account the average direction of motion. Weused a similar model as the well known XY spin model on a square lattice of linear size L, theparticles can move freely on the plane (an off-lattice model). A phase diagram in the space (φ,ξc) has been established where φ = ϕ/2 2 [0, π] and ξc being the critical noise. We shown thatξc strongly depends on the view’s angle φ 0.5π, but slightly varies with φ < 0.5π. So, we canconclude that the schooling behavior of animal is only of the prey species, but not of the predator