An exactly solvable lattice model for inhomogeneous interface growth

TL;DR

This paper presents an exactly solvable lattice model for inhomogeneous interface growth, revealing critical angles for cusp formation and Gaussian fluctuations, with implications for polymer physics.

Contribution

It introduces a new exactly solvable lattice model for inhomogeneous interface growth, providing explicit formulas and identifying a critical angle for cusp development.

Findings

Exact expressions for average height and fluctuations derived.

Identification of a critical angle for cusp formation.

Gaussian fluctuations around the mean interface shape.

Abstract

We study the dynamics of an exactly solvable lattice model for inhomogeneous interface growth. The interface grows deterministically with constant velocity except along a defect line where the growth process is random. We obtain exact expressions for the average height and height fluctuations as functions of space and time for an initially flat interface. For a given defect strength there is a critical angle between the defect line and the growth direction above which a cusp in the interface develops. In the mapping to polymers in random media this is an example for the transverse Meissner effect. Fluctuations around the mean shape of the interface are Gaussian.