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

Omar Al Hammal·Francisco de los Santos·Miguel A. Munoz
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Abstract

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 order-parameter, 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.

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Omar Al Hammal, Francisco de los Santos, Miguel A. Munoz. 2005-10-03. Non-order parameter Langevin equation for a bounded Kardar-Parisi-Zhang universality class. https://doi.org/10.1088/1742-5468%2F2005%2F10%2Fp10013

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