Critical behavior of a bounded Kardar-Parisi-Zhang equation

TL;DR

This paper investigates the critical behavior of a bounded KPZ equation with multiplicative noise, analyzing phase transitions between pinned and depinned states through theoretical and numerical methods, highlighting unique universality class features.

Contribution

It provides a detailed analysis of a bounded KPZ universality class with attractive walls, combining mean field, field theory, and numerical studies to uncover its critical properties.

Findings

Identified phase transition between pinned and depinned phases.

Characterized critical exponents and universality class features.

Analyzed effects of attractive walls on the transition.

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.