SOC in a class of sandpile models with stochastic dynamics

TL;DR

This study investigates a one-dimensional stochastic sandpile model, revealing nonuniversal avalanche scaling exponents dependent on a parameter, while surface roughness remains universally consistent across different conditions.

Contribution

It introduces a stochastic cellular automaton sandpile model with a tunable parameter, analyzing its scaling properties and demonstrating both nonuniversal avalanche exponents and universal surface roughness.

Findings

Power-law avalanche size distribution with exponents depending on lambda

Universal surface roughness exponent of approximately 1.75

Temporal mass spectrum with an exponent close to 2

Abstract

We have studied one-dimensional cellular automata with updating rules depending stochastically on the difference of the heights of neighbouring cells. The probability for toppling depends on a parameter lambda which goes to one with increasing slope, i.e. the dynamics can be varied continuously. We have investigated the scaling properties of the model using finite-size scaling analysis. A robust power-law behavior is observed for the probability density of the size of avalanches in a certain range of lambda values. The two exponents which determine the dependence of the probability density on time and system size both depend continuously on lambda, i.e. the model exhibits nonuniversal behavior. We also measured the roughness of the surface of the sandpile and here we obtained an universal behavior, i.e. a roughness exponent of about 1.75 for all values of lambda. For the temporal behavior of the mass a $f^{-\phi}$ spectrum is obtained with an exponent phi close to 2 again for all lambda-values.