Equivalence between the Abelian sandpile model and the q→0 limit of the Potts model

S.N. Majumdar and Deepak Dhar

Physica A: Statistical Mechanics and its Applications, 1992, vol. 185, issue 1, 129-145

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 = 85. We relate this exponent to the conventional exponents characterizing the distributions of avalanche sizes.

Date: 1992
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:185:y:1992:i:1:p:129-145

DOI: 10.1016/0378-4371(92)90447-X

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