UNIVERSALITY ASPECTS OF SELF-ORGANIZATION MODELS

Abstract

A sandpile model on the square lattice with periodic boundary conditions is studied as a problem of variable density of grains per site. We define an order parameter and we show the existence of a critical density. This model is the closed version of the deterministic BTW model and belongs to the "Fixed Energy Sandpiles" class. An algorithm identifying the periodic states of the system permits us to have a good estimation of the order parameter, which is free from transient effects. The universality of the model with respect to two different forms of oriented flows is studied and compared with that of the isotropic flow. We find two universality classes characterized by different critical exponents. The Manhattan flow appears to belong to the same universality class as the isotropic flow. However, the directed flow gives a completely different critical behavior. The complexity of the model for densities larger than the critical is also studied. It is observed that, both the Manhattan model and the isotropic model have an interesting structure characterized by several plateaus. The right edges of these plateaus are characterized by a sudden increase of the order parameter, giving rise to new critical points. The directed flow model has a simple structure without plateaus.