Modified Renormalization Strategy for Sandpile Models

TL;DR

This paper introduces a simplified renormalization approach for sandpile models that improves the calculation of the critical dynamical exponent, aligning well with existing numerical and theoretical findings.

Contribution

It proposes a new renormalization strategy that simplifies the analysis of sandpile models and accurately determines the critical exponent z.

Findings

The fixed point has a unique nonzero dynamical component.

The method yields critical exponent values consistent with previous results.

Simplifies the computation of the dynamical critical exponent.

Abstract

Following the Renormalization Group scheme recently developed by Pietronero {\it et al}, we introduce a simplifying strategy for the renormalization of the relaxation dynamics of sandpile models. In our scheme, five sub-cells at a generic scale $b$ form the renormalized cell at the next larger scale. Now the fixed point has a unique nonzero dynamical component that allows for a great simplification in the computation of the critical exponent $z$. The values obtained are in good agreement with both numerical and theoretical results previously reported.