Exact Mapping of the Stochastic Field Theory for Manna Sandpiles to Interfaces in Random Media

Pierre Le Doussal and Kay Jörg Wiese
Phys. Rev. Lett. 114, 110601 – Published 18 March 2015

Abstract

We show that the stochastic field theory for directed percolation in the presence of an additional conservation law [the conserved directed-percolation (C-DP) class] can be mapped exactly to the continuum theory for the depinning of an elastic interface in short-range correlated quenched disorder. Along one line of the 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 this 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.

  • Received 30 October 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.110601

© 2015 American Physical Society

Authors & Affiliations

Pierre Le Doussal and Kay Jörg Wiese

  • CNRS-Laboratoire de Physique Théorique de l’Ecole Normale Supérieure, 24 rue Lhomond, Paris 75005, France

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Issue

Vol. 114, Iss. 11 — 20 March 2015

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