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In this work, we consider a group of shes as the particles, but we assumed that only the individuals of its neighbors within a circle sector with central angle φ (is called angle of view) and radius R, are taken into account the average direction of motion. We used a similar model as the well known XY spin model on a square lattice of linear size L, the particles can move freely on the plane (an o -lattice model). | Communications in Physics, Vol. 23, No. 2 (2013), pp. 121-125 STUDY ON THE PHASE TRANSITION BEHAVIOR OF FISHES SCHOOLING SYSTEM NGUYEN PHUOC THE Department of Natural Science, Duy Tan University, K7/25 Quang Trung, Hai Chau, Da Nang, Vietnam LEE SANG-HEE Division of Fusion and Convergence of Mathematical Sciences, National Institute for Mathematical Sciences, Daejeon, Republic of Korea NGO VAN THANH AND NGUYEN AI VIET Institute of Physics, Vietnam Academy of Science and Technology 10 Dao Tan, Ba Dinh, Hanoi, Vietnam Email: nvthanh@iop.vast.ac.vn Received 25 May 2013 Accepted for publication 08 June 2013 The Vicsek's model (VM) [T. Vicsek, et. al., Phys. Rev. Lett. 75 (1995) 1226] is a popular 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 particles within a circle of radius R. In this work, we consider a group of shes as the particles, but we assumed that only the individuals of its neighbors within a circle sector with central angle φ (is called angle of view) and radius R, are taken into account the average direction of motion. We used a similar model as the well known XY spin model on a square lattice of linear size L, the particles can move freely on the plane (an o -lattice model). A phase diagram in the space (ϕ, ξc ) has been established where ϕ = φ/2 ∈ [0, π] and ξc being the critical noise. We showed that ξc strongly depends on the view's angle ϕ ≥ 0.5π , but slightly varies with ϕ 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 ϕ = 0.1π ϕ = 0.5π ϕ = 1.0π 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 ξ Fig. 2. Order parameter versus noise (squares) and 1.0π ξ for several values of (diamonds), with the system size 0.045 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 χO ϕ: 0.1π N = 100. (circles), 0.5π ϕ = 0.1π ϕ = 0.5π ϕ = 1.0π 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 ξ Fig. 3. The variance of the order parameter versus noise ϕ:
