Inversion Symmetry and Critical Exponents of Dissipating Waves in the Sandpile Model

TL;DR

This paper analyzes the statistics of dissipating waves in the sandpile model, revealing a power-law distribution with a critical exponent of 5/8 and establishing a relationship with boundary wave exponents through inversion symmetry.

Contribution

It provides an analytical and numerical study linking dissipating wave distributions to boundary wave exponents via inversion symmetry in the sandpile model.

Findings

Dissipating waves follow a power-law distribution with exponent 5/8.

The critical exponent is related to the last wave exponent through inversion symmetry.

The study combines analytical and numerical methods for validation.

Abstract

Statistics of waves of topplings in the Sandpile model is analysed both analytically and numerically. It is shown that the probability distribution of dissipating waves of topplings that touch the boundary of the system obeys power-law with critical exponent 5/8. This exponent is not indeendent and is related to the well-known exponent of the probability distribution of last waves of topplings by exact inversion symmetry s -> 1/s.