Conserved sandpile with a variable height restriction

TL;DR

This paper investigates a one-dimensional Oslo sandpile model with variable site heights, analyzing its critical behavior and phase transition using mean-field theory and Monte Carlo simulations.

Contribution

It introduces a variable height restriction in the Oslo sandpile model and characterizes its critical properties through finite-size scaling analysis.

Findings

Determined the critical particle density for the model.

Estimated critical exponents via finite-size scaling.

Validated mean-field and Monte Carlo results against each other.

Abstract

We study a restricted-height version of the one-dimensional Oslo sandpile with conserved density, using periodic boundary conditions. Each site has a limiting height which can be either two or three. When a site reaches its limiting height it becomes active and may topple, loosing two particles, which move randomly to nearest-neighbor sites. After a site topples it is randomly assigned a new limiting height. We study the model using mean-field theory and Monte Carlo simulation, focusing on the quasi-stationary state, in which the number of active sites fluctuates about a stationary value. Using finite-size scaling analysis, we determine the critical particle density and associated critical exponents.