Directed Percolation with a Conserved Field and the Depinning Transition

TL;DR

This paper presents an alternative derivation of the conserved directed-percolation (C-DP) field theory, clarifies its relation to the depinning transition, and demonstrates the redundancy of a previously problematic term using renormalization group analysis.

Contribution

It offers a new derivation method for the C-DP field theory and clarifies the relevance of a key term in the functional, strengthening the universality connection with depinning transitions.

Findings

C-DP and depinning transitions share the same universality class.

The problematic term in the field theory is shown to be redundant.

The new derivation avoids the disadvantages of the Doi-shift.

Abstract

Conserved directed-percolation (C-DP) and the depinning transition of a disordered elastic interface belong to the same universality class as has been proven very recently by Le Doussal and Wiese [Phys. Rev. Lett.~\textbf{114}, 110601 (2015)] through a mapping of the field theory for C-DP onto that of the quenched Edwards-Wilkinson model. Here, we present an alternative derivation of the C-DP field theoretic functional, starting with the coherent state path integral formulation of the C-DP and then applying the Grassberger-transformation, that avoids the disadvantages of the so-called Doi-shift. We revisit the aforementioned mapping with focus on a specific term in the field theoretic functional that has been problematic in the past when it came to assessing its relevance. We show that this term is redundant in the sense of the renormalization group.