Effect of Long-Range Interactions in the Conserved Kardar-Parisi-Zhang Equation

TL;DR

This paper investigates how long-range nonlinear interactions influence the behavior of the conserved Kardar-Parisi-Zhang equation, revealing new fixed points, phase transitions, and effects on surface roughness.

Contribution

It introduces a dynamic renormalization group analysis of the conserved KPZ equation with long-range interactions, identifying new fixed points and phase transition behaviors.

Findings

Long-range interactions lead to new fixed points with varying exponents.

Surface roughness decreases with long-range interactions, becoming smooth at d=2.

Distinct phase transitions depend on interaction strength and substrate dimension.

Abstract

The conserved Kardar-Parisi-Zhang equation in the presence of long-range nonlinear interactions is studied by the dynamic renormalization group method. The long-range effect produces new fixed points with continuously varying exponents and gives distinct phase transitions, depending on both the long-range interaction strength and the substrate dimension $d$. The long-range interaction makes the surface width less rough than that of the short-range interaction. In particular, the surface becomes a smooth one with a negative roughness exponent at the physical dimension d=2.