Self-Organizing Height-Arrow Model: Numerical and Analytical Results

Details Self-Organizing Height-Arrow Model: Numerical and Analytical Results Self-Organizing Height-Arrow Model: Numerical and Analytical Results

1997-08-02

arxiv.org/abs/cond-mat/9708015v1

Physics

Condensed Matter

Statistical Mechanics

14 pages, RevTeX, 12 Postscript and 4 RevTex figures, additional information available at http://thsun1.jinr.ru/~shcher

Scientific paper

The recently introduced self-organizing height-arrow (HA) model is numerically investigated on the square lattice and analytically on the Bethe lattice. The concentration of occupied sites and critical exponents of distributions of avalanches are evaluated for two slightly different versions of the model. The obtained exponents for distributions of avalanches by mass, area, duration and appropriate fractal dimensions are close to those for the BTW model, which suggests that the HA model belongs to the same universality class. For comparison, the concentration of occupied sites in the HA model is calculated exactly on the Bethe lattice of coordination number $q=4$ as well.

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