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Critical behavior of a bounded Kardar-Parisi-Zhang equation

Miguel A. Munoz·F. de los Santos·A. Achahbar
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Abstract

A host of spatially extended systems, both in physics and in other disciplines, are well described at a coarse-grained scale by a Langevin equation with multiplicative-noise. Such systems may exhibit non-equilibrium phase transitions, which can be classified into universality classes. Here we study in detail one of such classes that can be mapped into a Kardar-Parisi-Zhang (KPZ) interface equation with a positive (negative) non-linearity in the presence of a bounding lower (upper) wall. The wall limits the possible values taken by the height variable, introducing a lower (upper) cut-off, and induce a phase transition between a pinned (active) and a depinned (absorbing) phase. This transition is studied here using mean field and field theoretical arguments, as well as from a numerical point of view. Its main properties and critical features, as well as some challenging theoretical difficulties, are reported. The differences with other multiplicative noise and bounded-KPZ universality classes are stressed, and the effects caused by the introduction of ``attractive'' walls, relevant in some physical contexts, are also analyzed.

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Miguel A. Munoz, F. de los Santos, A. Achahbar. 2003-04-10. Critical behavior of a bounded Kardar-Parisi-Zhang equation. https://doi.org/10.1590/s0103-97332003000300005

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