Universality class of one-dimensional directed sandpile models.
A general n-state directed "sandpile" model is introduced. The stationary properties of the n-state model are derived for n<infinity, and analytical arguments based on a central limit theorem show that the model belongs to the universality class of the totally asymmetric Oslo model, with a crossover to uncorrelated branching process behavior for small system sizes. Hence, the central limit theorem allows us to identify the existence of a large universality class of one-dimensional directed sandpile models.
Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom. ms599@imperial.ac.uk
Matthew
M
Stapleton
Kim
K
Christensen