Critical Dynamics of Self-Organizing Eulerian Walkers

TL;DR

This paper investigates the critical dynamics of self-organizing Eulerian walkers on a square lattice, calculating critical exponents and demonstrating universality across different dynamical rules.

Contribution

It introduces a numerical analysis of Eulerian walker models, determining critical exponents and showing they belong to the same universality class.

Findings

Critical exponents for step and site distributions are approximately 1.75.

Both dynamical rules exhibit the same universality class.

Finite-size scaling analysis confirms the critical behavior.

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 ($\tau_l$) and visited sites ($\tau_s$) 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 $\tau_l=\tau_s=1.75\pm 0.1$.