Universality classes in the random-storage sandpile model

TL;DR

This paper investigates a stochastic sandpile model with probabilistic toppling, revealing that its universality class depends on the toppling probability p, transitioning from directed percolation to BTW universality class at a critical point p_c.

Contribution

It identifies the universality classes of the stochastic sandpile model across different probabilities, linking the transition to directed percolation and BTW classes.

Findings

For 0<p<p_c, the model belongs to the directed percolation universality class.

For p_c<p<1, the model belongs to the BTW universality class.

The critical probability p_c corresponds to the directed percolation threshold.

Abstract

The avalanche statistics in a stochastic sandpile model where toppling takes place with a probability p is investigated. The limiting case p=1 corresponds to the Bak-Tang-Wiesenfeld (BTW) model with deterministic toppling rule. Based on the moment analysis of the distribution of avalanche sizes we conclude that for 0<p<p_c the model belongs to the DP universality class while for p_c<p<1 it belongs to the BTW universality class, where p_c is identified with the critical probability for directed percolation in the corresponding lattice.