Determination of Finite Size Effect in Lattice Models From the Local Height Difference Distribution

Abstract

Growth of interfaces during vapor deposition is analyzed on a discrete lattice. It leads to finding distribution of local heights, measurable for any lattice model. Invariance in the change of this distribution in time is used to determine the finite size effects in various models The analysis is applied to the discrete linear growth equation and Kardar-Parisi-Zhang (KPZ) equation. A new model is devised that shows early convergence to the KPZ dynamics. Various known conservative and non conservative models are tested on a one dimensional substrate by comparing the growth results with the exact KPZ and linear growth equation results. The comparison helps in establishing the condition that helps in determining the presence of finite size effect for the given model. The new model is used in 2+1 dimensions to predict close to the true value of roughness constant for KPZ equation.