Direct evidence for conformal invariance of avalanche frontiers in sandpile models

Saberi, A.A ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevE.79.031121
  3. Publisher: 2009
  4. Abstract:
  5. Appreciation of stochastic Loewner evolution (SLEκ), 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 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. 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. © 2009 The American Physical Society
  6. Keywords:
  7. Abelian sandpile models ; Conformal invariances ; Critical systems ; Diffusivities ; Geometrical features ; Invariant properties ; Random walks ; Sand-pile models ; Stochastic loewner evolutions ; Conformal mapping ; Fractal dimension ; Sand
  8. Source: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics ; Volume 79, Issue 3 , Volume 79, Issue 3 , 2009 ; 15393755 (ISSN)
  9. URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.79.031121