Stochastic Model in the Kardar-Parisi-Zhang Universality With Minimal Finite Size Effects

TL;DR

This paper introduces a solid-on-solid lattice model for growth with minimal finite size effects, accurately reproducing KPZ universality class exponents in one dimension and extending results to higher dimensions.

Contribution

The paper presents a new lattice model that minimizes finite size effects and reproduces KPZ exponents, applicable in any dimension.

Findings

The model's roughness exponent matches KPZ predictions in 1D.

Finite size effects are minimized by observing time-invariant local height fluctuations.

Results extend to 2D and 3D substrates, showing the model's versatility.

Abstract

We introduce a solid on solid lattice model for growth with conditional evaporation. A measure of finite size effects is obtained by observing the time invariance of distribution of local height fluctuations. The model parameters are chosen so that the change in the distribution in time is minimum. On a one dimensional substrate the results obtained from the model for the roughness exponent $\alpha$ from three different methods are same as predicted for the Kardar-Parisi-Zhang (KPZ) equation. One of the unique feature of the model is that the $\alpha$ as obtained from the structure factor $S(k,t)$ for the one dimensional substrate growth exactly matches with the predicted value of 0.5 within statistical errors. The model can be defined in any dimensions. We have obtained results for this model on a 2 and 3 dimensional substrates.