Dynamic Renormalization Group Approach to Self-Organized Critical Phenomena

TL;DR

This paper applies the dynamic renormalization group to analyze two models of self-organized criticality, demonstrating they share the same universality class and estimating critical exponents.

Contribution

It introduces a systematic dynamic renormalization group approach to compare different self-organized critical models and estimate their critical exponents.

Findings

Both models belong to the same universality class.

Critical exponents are estimated up to one loop order.

The models' behavior under parity transformation does not affect their universality.

Abstract

Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that they both belong to the same universality class, in agreement with computer simulations. The asymptotic values of the critical exponents are estimated up to one loop order from a systematic expansion of a nonlinear equation in the number of coupling constants.