Data di Pubblicazione:
2012
Citazione:
Exact integration for height probabilities in the abelian sandpile model / S. Caracciolo, A. Sportiello. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2012:09(2012), pp. P09013.P09013.1-P09013.P09013.14.
Abstract:
The height probabilities for the recurrent configurations in the Abelian Sandpile model on the square lattice have analytic expressions, in terms of multidimensional quadratures. At first, these quantities were evaluated numerically with high accuracy and conjectured to be certain cubic rational- coefficient polynomials in 1/π. Later their values were determined by different methods.
We revert to the direct derivation of these probabilities, by computing analytically the corresponding integrals. Once again, we confirm the predictions on the probabilities, and thus, as a corollary, the conjecture on the average height, ⟨ρ⟩ = 17/8.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
sandpile models (theory)
Elenco autori:
S. Caracciolo, A. Sportiello
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