Breakdown of Simple Scaling in Abelian Sandpile Models in One Dimension

Details Breakdown of Simple Scaling in Abelian Sandpile Models in One Dimension Breakdown of Simple Scaling in Abelian Sandpile Models in One Dimension

1994-12-16

arxiv.org/abs/cond-mat/9412085v1

Phys. Rev E51 (1995) R2705.

Physics

Condensed Matter

10 pages, revtex, figures included

Scientific paper

10.1103/PhysRevE.51.R2705

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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