Fractal properties of relaxation clusters and phase transition in a stochastic sandpile automaton

TL;DR

This paper investigates how the spatial structure of relaxation clusters in a stochastic sandpile automaton changes at a phase transition, revealing a loss of fractal properties as the system transitions from critical to non-critical states.

Contribution

It introduces a stochastic sandpile automaton model incorporating static friction effects and analyzes the fractal properties of relaxation clusters across a phase transition.

Findings

Relaxation clusters are fractal below the critical point p_c.

At p=p_c, the fractal nature of clusters disappears.

The phase transition is continuous and affects the spatial properties of the system.

Abstract

We study numerically the spatial properties of relaxation clusters in a two dimensional sandpile automaton with dynamic rules depending stochastically on a parameter p, which models the effects of static friction. In the limiting cases p=1 and p=0 the model reduces to the critical height model and critical slope model, respectively. At p=p_c, a continuous phase transition occurs to the state characterized by a nonzero average slope. Our analysis reveals that the loss of finite average slope at the transition is accompanied by the loss of fractal properties of the relaxation clusters.