Renormalization Group Study of Sandpile on the Triangular Lattice

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 $τ=1.36$. The probabilities of the sand transition are compared with the branching probabilities of the spanning trees on the triangular lattice which are also evaluated.