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

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 $α$ 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 $α$ 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.