1995/04/06 by Brigita Kutjnak-Urbanc, Kutjnak-Urbanc, Brigita, Stefano Zapperi +5
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Condensed Matter (cond-mat) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.cond-mat/9504022
openalex publication_date 1995/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the sandpile model on the two--dimensional Sierpinski gasket fractal. We find that the model displays novel critical behavior, and we analyze the distribution functions of avalanche sizes, lifetimes and topplings and calculate the associated critical exponents τ= 1.51 ± 0.04, α= 1.63 ± 0.04 and μ= 1.36 ± 0.04. The avalanche size distribution shows power law behavior modulated by logarithmic oscillations which can be related to the discrete scale invariance of the underlying lattice. Such a distribution can be formally described by introducing a complex scaling exponent τ* ≡ τ+ i δ, where the real part τ corresponds to the power law and the imaginary part δ is related to the period of the logarithmic oscillations.