An exact mapping of the stochastic field theory for Manna sandpiles to interfaces in random media

TL;DR

This paper establishes an exact theoretical mapping between the stochastic field theory of Manna sandpiles and the continuum theory of elastic interface depinning in disordered media, revealing their shared universality class.

Contribution

It provides the first exact mapping between the C-DP class of stochastic sandpiles and the depinning of elastic interfaces, clarifying their universal behavior.

Findings

Manna sandpiles and elastic interface depinning share the same universality class.

The mapping simplifies the dynamics to overdamped motion on a specific parameter line.

Additional memory terms do not alter the universality class.

Abstract

We show that the stochastic field theory for directed percolation in presence of an additional conservation law (the C-DP class) can be mapped exactly to the continuum theory for the depinning of an elastic interface in short-range correlated quenched disorder. On one line of parameters commonly studied, this mapping leads to the simplest overdamped dynamics. Away from this line, an additional memory term arises in the interface dynamics; we argue that it does not change the universality class. Since C-DP is believed to describe the Manna class of self-organized criticality, this shows that Manna stochastic sandpiles and disordered elastic interfaces (i.e. the quenched Edwards-Wilkinson model) share the same universal large-scale behavior.