Roughening of $k$-mer growing interfaces in stationary regimes

TL;DR

This paper investigates the steady state behavior of interfaces in solid-on-solid growth models involving extended particles, revealing universal scaling properties similar to monomer interfaces despite complex dynamics.

Contribution

It introduces a mapping of $k$-mer interface dynamics onto an exclusion process, enabling analysis of roughening exponents and distributions in stationary regimes.

Findings

Universal scaling behavior observed for $k$-mer interfaces.

Roughening exponents and height distributions can be computed directly.

Dynamics partitioned into many sectors, yet results suggest common scaling laws.

Abstract

We discuss the steady state dynamics of interfaces with periodic boundary conditions arising from body-centered solid-on-solid growth models in $1+1$ dimensions involving random aggregation of extended particles (dimers, trimers,\,$\cdots,k$-mers). Roughening exponents as well as width and maximal height distributions can be evaluated directly in stationary regimes by mapping the dynamics onto an asymmetric simple exclusion process with $k$-\,type of vacancies. Although for $k \ge 2$ the dynamics is partitioned into an exponentially large number of sectors of motion, the results obtained in some generic cases strongly suggest a universal scaling behavior closely following that of monomer interfaces.