Teoria de campo médio para um modelo de Vicsek em rede

Abstract

Active matter is a group of individuals that continuously consume energy to move in the enviroment. They are found in nature at different scales, for example flocks of birds and colonies of bacteria, and outside the biological field, systems such as a collection of vibrating motors. Despite the clear differences between these systems, they have in common the emergence of collective motion. Understanding how collective motion arises is the main goal of the study of active matter. The Vicsek model was the first to obtain results consistent with observations of groups of self-propelled organisms, showing that the emergence of collective behavior can be treated as a phase transition dependent on density and noise, and whose order parameter is associated with the velocity of particles. From it, new models with different features were created showing a rich variety of behaviors that can arise in the dynamics of interacting self-propelled individuals. In this work I study the behavior of an active matter model on a triangular lattice subject to an alignment interaction, and to excluded volume, using a mean-field approximation. Analyzing the evolution of the probabilities for the occupation of sites in the lattice, we find that the model goes through a discontinuous phase transition in which a particular direction of motion dominates.