Directed d-mer diffusion describing Kardar-Parisi-Zhang type of surface growth

TL;DR

This paper maps surface growth models to driven lattice gases of d-mers, enabling efficient simulations that support the Kardar-Parisi-Zhang universality class in multiple dimensions, with new large-scale numerical evidence.

Contribution

It introduces a novel mapping of surface growth to driven lattice gases, allowing large-scale simulations and providing new numerical estimates of scaling exponents in higher dimensions.

Findings

Scaling exponents increase with system size.

Evidence supports KPZ universality in 2+1 dimensions.

Numerical results challenge some theoretical predictions in 3+1 dimensions.

Abstract

We show that d+1-dimensional surface growth models can be mapped onto driven lattice gases of d-mers. The continuous surface growth corresponds to one dimensional drift of d-mers perpendicular to the (d-1)-dimensional "plane" spanned by the d-mers. This facilitates efficient, bit-coded algorithms with generalized Kawasaki dynamics of spins. Our simulations in d=2,3,4,5 dimensions provide scaling exponent estimates on much larger system sizes and simulations times published so far, where the effective growth exponent exhibits an increase. We provide evidence for the agreement with field theoretical predictions of the Kardar-Parisi-Zhang universality class and numerical results. We show that the (2+1)-dimensional exponents conciliate with the values suggested by Lassig within error margin, for the largest system sizes studied here, but we can't support his predictions for (3+1)d numerically.