The Abelian Manna model on two fractal lattices

Abstract

We analyze the avalanche size distribution of the Abelian Manna model on two different fractal lattices with the same dimension d_g=ln(3)/ln(2), with the aim to probe for scaling behavior and to study the systematic dependence of the critical exponents on the dimension and structure of the lattices. We show that the scaling law D(2-tau)=d_w generalizes the corresponding scaling law on regular lattices, in particular hypercubes, where d_w=2. Furthermore, we observe that the lattice dimension d_g, the fractal dimension of the random walk on the lattice d_w, and the critical exponent D, form a plane in 3D parameter space, i.e. they obey the linear relationship D=0.632(3) d_g + 0.98(1) d_w - 0.49(3).

arXiv comment4 pages, 3 figures, 3 tables, submitted to PRE as a Brief Report

References in corpus (6)

• Universal scaling behavior of non-equilibrium phase transitions
• The abelian sandpile and related models
• Universality in Sandpile Models
• Universality in sandpiles
• Critical properties of Ising model on Sierpinski fractals. A finite size scaling analysis approach
• Reaction-diffusion system with self-organized critical behavior

Cited by in corpus (4)

• Abelian Manna model on various lattices in one and two dimensions
• Non-Perturbative Renormalization Group for the Diffusive Epidemic Process
• Universality and a numerical ε-expansion of the Abelian Manna model below upper critical dimension
• Critical properties of deterministic and stochastic sandpile models on two-dimensional percolation backbone