Particle-hole symmetry in a sandpile model

TL;DR

This paper explores a sandpile model incorporating both particle and hole avalanches, revealing critical behavior and non-trivial correlations at the symmetric point where particle and hole creation probabilities are equal.

Contribution

It introduces a combined particle-hole sandpile model and analyzes its critical behavior and correlations at the symmetry point.

Findings

System is critical for all p except at p=1/2

At p=1/2, the system exhibits non-trivial correlations

The power spectrum at p=1/2 shows 1/f type behavior

Abstract

In a sandpile model addition of a hole is defined as the removal of a grain from the sandpile. We show that hole avalanches can be defined very similar to particle avalanches. A combined particle-hole sandpile model is then defined where particle avalanches are created with probability $p$ and hole avalanches are created with the probability $1-p$. It is observed that the system is critical with respect to either particle or hole avalanches for all values of $p$ except at the symmetric point of $p_c=1/2$. However at $p_c$ the fluctuating mass density is having non-trivial correlations characterized by $1/f$ type of power spectrum.