Critical Dynamics of Self-Organizing Eulerian Walkers

Abstract

The model of self-organizing Eulerian walkers is numerically investigated on the square lattice. The critical exponents for the distribution of a number of steps ($τ_l$) and visited sites ($τ_s$) characterizing the process of transformation from one recurrent configuration to another are calculated using the finite-size scaling analysis. Two different kinds of dynamical rules are considered. The results of simulations show that both the versions of the model belong to the same class of universality with the critical exponents $τ_l=τ_s=1.75\pm 0.1$.