Local Rigidity in Sandpile Models

TL;DR

This paper investigates how the concept of local rigidity influences sandpile models, showing that finite rigidity values effectively become infinite at large scales, distinguishing sandpile systems from diffusive ones.

Contribution

It introduces a renormalization group analysis demonstrating that finite local rigidity in sandpile models diverges at large scales, clarifying the fundamental difference from diffusive systems.

Findings

Finite rigidity renormalizes to infinity at the fixed point.

Large-scale behavior distinguishes sandpile from diffusive systems.

Numerical simulations support the analytical predictions.

Abstract

We address the problem of the role of the concept of local rigidity in the family of sandpile systems. We define rigidity as the ratio between the critical energy and the amplitude of the external perturbation and we show, in the framework of the Dynamically Driven Renormalization Group (DDRG), that any finite value of the rigidity in a generalized sandpile model renormalizes to an infinite value at the fixed point, i.e. on a large scale. The fixed point value of the rigidity allows then for a non ambiguous distinction between sandpile-like systems and diffusive systems. Numerical simulations support our analytical results.