Universality in Sandpile Models

TL;DR

This paper classifies sandpile models into universality classes based on extensive numerical simulations, revealing that different models, including the Manna and Bak-Tang-Wiesenfeld models, belong to distinct universality classes.

Contribution

It introduces a new classification scheme for sandpile models into universality classes based on numerical exponents.

Findings

Manna two-state model belongs to a distinct universality class from the original BTW model.

Directed sandpile models form a separate universality class including Dhar's model.

Extensive simulations measure exponents to differentiate classes.

Abstract

A new classification of sandpile models into universality classes is presented. On the basis of extensive numerical simulations, in which we measure an extended set of exponents, the Manna two state model [S. S. Manna, J. Phys. A 24, L363 (1991)] is found to belong to a universality class of random neighbor models which is distinct from the universality class of the original model of Bak, Tang and Wiesenfeld [P. Bak, C. Tang and K. Wiensenfeld, Phys. Rev. Lett. 59, 381 (1987)]. Directed models are found to belong to a universality class which includes the directed model introduced and solved by Dhar