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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.
The roughening of interfaces moving in inhomogeneous media is investigated by numerical integration of the phenomenological stochastic differential equation proposed by Kardar, Parisi, and Zhang [Phys. Rev. Lett. 56, 889, (1986)] with quenched noise
These lectures provide an introduction to the directed percolation and directed animals problems, from a physicists point of view. The probabilistic cellular automaton formulation of directed percolation is introduced. The planar duality of the diode
We study the nature of the synchronization transition in spatially extended systems by discussing a simple stochastic model. An analytic argument is put forward showing that, in the limit of discontinuous processes, the transition belongs to the dire
We introduce and solve a model of hardcore particles on a one dimensional periodic lattice which undergoes an active-absorbing state phase transition at finite density. In this model an occupied site is defined to be active if its left neighbour is o
We study directed rigidity percolation (equivalent to directed bootstrap percolation) on three different lattices: square, triangular, and augmented triangular. The first two of these display a first-order transition at p=1, while the augmented trian