Roughening transition and universality of single step growth models in (2+1)-dimensions

TL;DR

This study investigates a (2+1)-dimensional single step growth model, revealing a critical point where the system transitions from KPZ to EW universality classes, challenging previous assumptions.

Contribution

It identifies a critical parameter value for a roughening transition in the (2+1)-D single step model, supported by extensive numerical simulations.

Findings

Existence of a critical point p_c≈0.25 for the transition

Transition from KPZ to EW universality class

Validation through estimation of interface exponents

Abstract

We study (2+1)-dimensional single step model (SSM) for crystal growth including both deposition and evaporation processes parametrized by a single control parameter $p$. Using extensive numerical simulations with a relatively high statistics, we estimate various interface exponents such as roughness, growth and dynamic exponents as well as various geometric and distribution exponents of height clusters and their boundaries (or iso-height lines) as function of $p$. We find that, in contrary to the general belief, there exists a critical value $p_c\approx 0.25$ at which the model undergoes a roughening transition from a rough phase with $p<p_c$ in the Kardar-Parisi-Zhang (KPZ) universality to a smooth phase with $p>p_c$, asymptotically in the Edwards-Wilkinson (EW) class. We validate our conclusion by estimating the effective roughness exponents and their extrapolation to the infinite-size limit.