Transfer Matrix Method in Sandpile Models

TL;DR

This paper introduces a transfer matrix method tailored for solving certain sandpile models, successfully applying it to deterministic nonabelian cases for N=2 and N=3, and discusses potential generalizations.

Contribution

The paper develops a transfer matrix approach specifically for sandpile models and demonstrates its application to nonabelian cases, extending the analytical tools available for these systems.

Findings

Successfully solved nonabelian sandpile models for N=2 and N=3

Proposed a transfer matrix framework adaptable to other sandpile models

Discussed potential for generalization to arbitrary N

Abstract

We present a transfer matrix method which is particularly useful for solving some classes of sandpile models. The method is then used to solve the deterministic nonabelian sandpile models for N=2 and N=3. The possibility of generalization to arbitrary N is discussed briefly.