Path-integral representation for a stochastic sandpile

TL;DR

This paper develops an exact path-integral framework for a stochastic sandpile model, revealing its massless nature and cooperative diffusion dynamics, and introduces a perturbation series for activity density over time.

Contribution

It presents a novel operator and path-integral formalism for stochastic sandpiles, enabling analytical insights into their dynamics and perturbative calculations.

Findings

Model is massless and exhibits cooperative diffusion

Derived a series expansion for activity density

Provided a diagrammatic perturbation theory

Abstract

We introduce an operator description for a stochastic sandpile model with a conserved particle density, and develop a path-integral representation for its evolution. The resulting (exact) expression for the effective action highlights certain interesting features of the model, for example, that it is nominally massless, and that the dynamics is via cooperative diffusion. Using the path-integral formalism, we construct a diagrammatic perturbation theory, yielding a series expansion for the activity density in powers of the time.