A simple sandpile model of active-absorbing state transitions

TL;DR

This paper introduces a simple sandpile model to study active-absorbing state transitions, revealing distinct phases with unique correlations and critical behaviors different from known universality classes.

Contribution

It presents a new, minimal sandpile model demonstrating different critical behavior and correlation structures in active and absorbing phases.

Findings

Active phase has product measure

Absorbing phase exhibits nontrivial correlations

System relaxes slower than exponential to the absorbing phase

Abstract

We study a simple sandpile model of active-absorbing state transitions in which a particle can hop out of a site only if the number of particles at that site is above a certain threshold. We show that the active phase has product measure whereas nontrivial correlations are found numerically in the absorbing phase. It is argued that the system relaxes to the latter phase slower than exponentially. The critical behavior of this model is found to be different from that of the other known universality classes.