The abelian sandpile and related models

Dhar, Deepak (1999) The abelian sandpile and related models Physica A: Statistical Mechanics and its Applications, 263 (1-4). pp. 4-25. ISSN 0378-4371

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The Abelian sandpile model is the simplest analytically tractable model of self-organized criticality. This paper presents a brief review of known results about the model. The Abelian group structure of the algebra of operators allows an exact calculation of many of its properties. In particular, when there is a preferred direction, one can calculate all the critical exponents characterizing the distribution of avalanche-sizes in all dimensions. For the undirected case, the model is related to q → 0 state Potts model. This enables exact calculation of some exponents in two dimensions; there are some conjectures about others. We also discuss a generalization of the model to a network of communicating reactive processors. This includes sandpile models with stochastic toppling rules as a special case. We also consider a nondashAbelian stochastic variant, which lies in a different universality class; related to directed percolation.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:9285
Deposited On:29 Oct 2010 12:05
Last Modified:16 May 2016 19:06

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