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

Pierre Le Doussal (1) , Kay Jörg Wiese (1)

1 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

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.

Domaines: Physique [physics]; Matière Condensée [cond-mat]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]

Pierre Le Doussal, Kay Jörg Wiese. An exact mapping of the stochastic field theory for Manna sandpiles to interfaces in random media. Physical Review Letters, 2015, 114 (11), pp.110601. ⟨10.1103/PhysRevLett.114.110601⟩. ⟨hal-02281087⟩