Direct Evidence for Conformal Invariance of Avalanche Frontier in Sandpile Models

Details Direct Evidence for Conformal Invariance of Avalanche Frontier in Sandpile Models Direct Evidence for Conformal Invariance of Avalanche Frontier in Sandpile Models

2008-12-04

arxiv.org/abs/0812.0939v1

Phys.Rev.E79:031121,2009

Physics

Condensed Matter

Statistical Mechanics

6 pages, 4 figures

Scientific paper

10.1103/PhysRevE.79.031121

Appreciation of Stochastic Loewner evolution (SLE$_\kappa$), as a powerful tool to check for conformal invariant properties of geometrical features of critical systems has been rising. In this paper we use this method to check conformal invariance in sandpile models. Avalanche frontiers in Abelian sandpile model (ASM) are numerically shown to be conformally invariant and can be described by SLE with diffusivity $\kappa=2$. This value is the same as value obtained for loop erased random walks (LERW). The fractal dimension and Schramm's formula for left passage probability also suggest the same result. We also check the same properties for Zhang's sandpile model.

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