Model of crystal growth with simulated self-attraction

TL;DR

This paper introduces a (1+1)-dimensional kinetic model for crystal growth incorporating simulated self-attraction, revealing a new universality class of depinning transition with specific critical indices through Monte Carlo simulations.

Contribution

The study presents a novel kinetic model of crystal growth with self-attraction effects and characterizes its depinning transition and critical behavior.

Findings

The model exhibits a depinning transition with KPZ-type roughness.

Critical indices are identified: ν_parallel=0.82, ν_perp=0.55, growth velocity=1.08.

Critical properties are independent of the dynamics type.

Abstract

The (1+1)-dimensional kinetic model of crystal growth with simulated self-attraction and random sequential or parallel dynamics is introduced and studied via Monte-Carlo simulations. To imitate the attraction of absorbing atoms the probability of deposition is chosen to depend on the number of the nearest-neighbor atoms surrounding the deposited atom so it increases with this number. As well the evaporation probabilities are chosed to roughly account for this self-attraction. The model exhibits the interface depinning transition with KPZ-type roughness behavior in the moving phase. The critical indices of the correlation lengths are $\nu_\parallel = 0.82 \pm 0.03,{\rm{}}\nu_ \bot = 0.55 \pm 0.02$ and the critical index of the growth velocity is $1.08 \pm 0.03$ indicating the new universality class of the depinning transition. The critical properties of the model do not depend on the type of dynamics implemented.