Renormalization Group Study of Sandpile on the Triangular Lattice

TL;DR

This paper uses the renormalization group method to analyze the sandpile model on a triangular lattice, identifying a fixed point and calculating critical exponents and transition probabilities, validated by numerical simulations.

Contribution

It provides a detailed RG analysis of the sandpile on a triangular lattice, including fixed points, critical exponents, and transition probabilities, advancing understanding of self-organized criticality.

Findings

Identified a unique attractive fixed point.

Calculated the avalanche size distribution exponent as τ=1.36.

Compared transition probabilities with spanning tree branching probabilities.

Abstract

We apply the renormalization group approach to the sandpile on the triangular lattice. The only attractive fixed point is found. The obtained fixed point height probabilities are compared with numerical simulations. The value of critical exponent of avalanche size distribution is found to be $\tau=1.36$. The probabilities of the sand transition are compared with the branching probabilities of the spanning trees on the triangular lattice which are also evaluated.