Self-organised criticality in stochastic sandpiles: Connection to directed percolation

¹ Instituut voor Theoretische Fysica, KU Leuven - 3000 Leuven, Belgium
² CMP Division, Saha Institute of Nuclear Physics - 1/AF Bidhan Nagar, Kolkata-700064, India
³ Max-Planck-Institut für Physik komplexer Systeme - Nöthnitzer Strasse 38, 01187 Dresden, Germany

Received: 11 October 2014
Accepted: 1 December 2014

Abstract

We introduce a stochastic sandpile model where finite drive and dissipation are coupled to the activity field. The absorbing phase transition here, as expected, belongs to the directed percolation (DP) universality class. We focus on the small drive and dissipation limit, i.e. the so-called self-organised critical (SOC) regime and show that the system exhibits a crossover from ordinary DP scaling to a dissipation-controlled scaling which is independent of the underlying dynamics or spatial dimension. The new scaling regime continues all the way to the zero bulk drive limit suggesting that the corresponding SOC behaviour is only DP, modified by the dissipation-controlled scaling. We demonstrate this for the continuous and discrete Manna model driven by noise and bulk dissipation.