The system is put under a source of external perturbation called “noise”, the individuals can freely move from one site to another site on a two-dimension triangular lattice. We use the Monte-Carlo simulation technique for studying the behavior of the model with varying noise. For simplicity, we consider the orientation of individuals which has q states as in the Potts model. We show that the system has three phases which correspond to the uncollected, flocking and runaway behaviors at very low, medium and high noise, respectively. These phases are separated by two first-order transitions. | Communications in Physics, Vol. 25, No. 3 (2015), pp. 203-210 DOI: MONTE CARLO SIMULATION ON THE PHASE TRANSITION OF ANIMAL GROUP: A q-STATE POTTS MODEL NGUYEN PHUOC THE Department of Natural Science, Duy Tan University, K7/25 Quang Trung, Hai Chau, Da Nang, Vietnam NGO VAN THANH Institute of Physics - Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi, Vietnam Received 06 June 2015 Accepted for publication 03 September 2015 Abstract. We study in this work the phase transition behaviour of animal groups. We assume that the individuals in the group have two classes of state. One is the internal state which can be either excited or non-excited. The other one is characterized by their orientation or direction of motion, it is so called the external state. The internal state plays an important role in the rules of interaction between the individuals. The system is put under a source of external perturbation called “noise”, the individuals can freely move from one site to another site on a two-dimension triangular lattice. We use the Monte-Carlo simulation technique for studying the behavior of the model with varying noise. For simplicity, we consider the orientation of individuals which has q states as in the Potts model. We show that the system has three phases which correspond to the uncollected, flocking and runaway behaviors at very low, medium and high noise, respectively. These phases are separated by two first-order transitions. Keywords: collective behavior, phase transition, Monte-Carlo simulation, q-state Potts model. I. INTRODUCTION The collective behavior is a widely observed phenomenon in various of biological species. In particular the flocking behavior of animal groups. It is one of the main topics which have been extensively investigated during the last two decades using biological, mathematical and physical models. Well-known examples are found in populations such as large schools of fish, the .
