ON THE PROPERTIES OF THE ORDERED STATE FORMED IN THE VICSEK MODEL FOR THE DISPLACEMENT OF SELF-DRIVEN INDIVIDUALS 

GABRIEL BAGLIETTO, EZEQUIEL V. ALBANO

Pinamar Argentina

Workshop; DYSES 2009 IV MEETING ON DYNAMICS OF SOCIAL AND ECONOMIC SYSTEMS; 2009

Presentación Oral y publicación en libro de resúmenes.The Vicsek model (VM) [1], for the description of the collective behavior of self-driven individuals, assumes that each agent adopts the average direction of movement of its neighbors, perturbed by an external noise. Early simulations have shown the occurrence of a second-order transition between a state of ordered collective displacement (low-noise limit) and a disordered regime (high-noise limit) [1].  Due to its simplicity and minimal character, the VM is an excellent candidate for representing a broad universality class in the field of far-from-equilibrium critical systems.In order to understand the onset of long range order in the VM, we determined the network formed by the interaccions between individuals, by means of computer simulations, performed in d = 2 dimensions. The cluster size distribution and the degree of ordering inside each cluster were evaluated. The structural properties of the formed network, e.g. the average path length and the clustering coefficient [2], were also determined. The onset of order can be understood due to the large effective dimension of the formed network.  References:[1] Vicsek, T., A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet,  Phys. Rev. Lett. 75, 1226 (1995). [2]  R. Albert, A. B. Barabási, Rev. Mod. Phys. 74, 47 (2002).