arXiv subjects

E. Milshtein

Publications and source records attributed to E. Milshtein.

2 recordsLinked to original sources

arXiv1998

Symmetries and Universality Classes in Conservative Sandpile Models

The symmetry properties which determine the critical exponents and universality classes in conservative sandpile models are identified. This is done by introducing a set of models, including all possible combinations of abelian vs. non-abelian, deterministic vs. stochastic and isotropic vs. anisotropic toppling rules. The universality classes are determined by an extended set of critical exponents, scaling functions and geometrical features. Two universality classes are clearly identified: (a) the universality class of abelian models and (b) the universality class of stochastic models. In addition, it is found that non-abelian models with deterministic toppling rules exhibit non-universal behavior.

cond-mat↗

arXiv1998

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

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.

cond-mat.stat-mech↗