Direct evidence for conformal invariance of avalanche frontiers in sandpile models
A. A. Saberi, S. Moghimi-Araghi, H. Dashti-Naserabadi, S. Rouhani
2009
Physical Review E
Appreciation of Stochastic Loewner evolution (SLE_κ), 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 κ=2. This value is the same as value obtained for loop erased random walks (LERW). The
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... al 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.
doi:10.1103/physreve.79.031121
pmid:19391916
fatcat:7k7w5dsx7zborbdycu5di7zmtq