Non-order parameter Langevin equation for a bounded Kardar-Parisi-Zhang universality class

We introduce a Langevin equation describing the pinning-depinning phase transition experienced by Kardar-Parisi-Zhang interfaces in the presence of a bounding “lower-wall”. This provides a continuous description for this universality class, complementary to the different and already well documented one for the case of an “upper-wall”. The Langevin equation is written in terms of a field that is not an orderparameter, in contrast to standard approaches, and is studied both by employing a systematic mean-field approximation and by means of a recently introduced efficient integration scheme. Our findings are in good agreement with known results from microscopic models in this class, while the numerical precision is improved. This Langevin equation constitutes a sound starting point for further analytical calculations, beyond mean-field, needed to shed more light on this poorly understood universality class. PACS numbers: 05.40-a, 05.70.Jk, 05.70.Ln, 02.50.-r Submitted to: J. Stat. Mech.