Majumdar, S. N. ; Dhar, Deepak (1992) Equivalence between the Abelian sandpile model and the q→0 limit of the Potts model Physica A: Statistical Mechanics and its Applications, 185 (1-4). pp. 129-145. ISSN 0378-4371
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Official URL: http://linkinghub.elsevier.com/retrieve/pii/037843...
Related URL: http://dx.doi.org/10.1016/0378-4371(92)90447-X
Abstract
We establish an equivalence between the undirected Abelian sandpile model and the q→0 limit of the q-state Potts model. The equivalence is valid for arbitrary finite graphs. Two-dimensional Abelian sandpile models, thus, correspond to a conformal field theory with central charge c = -2. The equivalence also gives a Monte Carlo algorithm to generate random spanning trees. We study the growth process of the spread of fire under the burning algorithm in the background of a random recurrent configuration of the Abelian sandpile model. The average number of sites burnt upto time t varies at ta. In two dimensions our numerically determined value of a agrees with the theoretical prediction a=8/5 . We relate this exponent to the conventional exponents characterizing the distributions of avalanche sizes.
Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |
ID Code: | 9276 |
Deposited On: | 29 Oct 2010 11:53 |
Last Modified: | 08 Feb 2011 08:53 |
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