Universality Classes in Isotropic, Abelian and non-Abelian, Sandpile Models

TL;DR

This study uses extensive simulations to analyze the critical behavior of isotropic sandpile models, revealing that abelian and non-abelian models belong to distinct universality classes based on critical exponents and avalanche features.

Contribution

It provides a comprehensive numerical comparison of abelian and non-abelian sandpile models, identifying their belonging to different universality classes.

Findings

Abelian and non-abelian models exhibit different critical exponents.

Avalanche geometric features differ significantly between models.

Scaling functions reveal distinct temporal evolution patterns.

Abstract

Universality in isotropic, abelian and non-abelian, sandpile models is examined using extensive numerical simulations. To characterize the critical behavior we employ an extended set of critical exponents, geometric features of the avalanches, as well as scaling functions describing the time evolution of average quantities such as the area and size during the avalanche. Comparing between the abelian Bak-Tang-Wiesenfeld model [P. Bak, C. Tang and K. Wiensenfeld, Phys. Rev. Lett. 59, 381 (1987)], and the non-abelian models introduced by Manna [S. S. Manna, J. Phys. A. 24, L363 (1991)] and Zhang [Y. C. Zhang, Phys. Rev. Lett. 63, 470 (1989)] we find strong indications that each one of these models belongs to a distinct universality class.