Dynamical properties of the Zhang model of Self-Organized Criticality

TL;DR

This paper analyzes the dynamical properties and critical exponents of the Zhang model of self-organized criticality in 2D and 3D, revealing differences from the abelian model and discussing implications for theoretical approaches.

Contribution

It provides new computed critical exponents for the Zhang model, compares them with other models, and discusses the relationship between different dynamical exponents.

Findings

3D exponents differ from the abelian model

Dynamical exponent from correlation length and roughness may differ

New quantities with computed critical exponents are presented

Abstract

Critical exponents of the infinitely slowly driven Zhang model of self-organized criticality are computed for $d=2,3$ with particular emphasis devoted to the various roughening exponents. Besides confirming recent estimates of some exponents, new quantities are monitored and their critical exponents computed. Among other results, it is shown that the three dimensional exponents do not coincide with the Bak, Tang, and Wiesenfeld (abelian) model and that the dynamical exponent as computed from the correlation length and from the roughness of the energy profile do not necessarily coincide as it is usually implicitly assumed. An explanation for this is provided. The possibility of comparing these results with those obtained from Renormalization Group arguments is also briefly addressed.