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Breakdown of Simple Scaling in Abelian Sandpile Models in One Dimension

Agha Afsar Ali·Deepak Dhar
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Abstract

We study the abelian sandpile model on decorated one dimensional chains. We determine the structure and the asymptotic form of distribution of avalanche-sizes in these models, and show that these differ qualitatively from the behavior on a simple linear chain. We find that the probability distribution of the total number of topplings $s$ on a finite system of size $L$ is not described by a simple finite size scaling form, but by a linear combination of two simple scaling forms $Prob_L(s) = 1/L f_1(s/L) + 1/L^2 f_2(s/L^2)$, for large $L$, where $f_1$ and $f_2$ are some scaling functions of one argument.

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Agha Afsar Ali, Deepak Dhar. 1994-12-16. Breakdown of Simple Scaling in Abelian Sandpile Models in One Dimension. https://doi.org/10.1103/physreve.51.r2705

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