Review on Relationship Between the Universality Class of the Kardar-Parisi-Zhang Equation and the Ballistic Deposition Model

Abstract

We have analysed the research findings on the universality class and discussed the connection between the Kardar-Parisi-Zhang (KPZ) universality class and the ballistic deposition model in microscopic rules. In one dimension and 1+1 dimensions deviations are not important in the presence of noise. At the same time, they are very relevant for higher dimensions or deterministic evolution. Mostly, in the analyses a correction scale higher than 1280 has not been studied yet. Therefore, the growth of the interface for finite system size β ≥ 0.30 value predicted by the KPZ universality class is still predominant. Also, values of α ≥ 0.40, β ≥ 0.30, and z ≥ 1.16 obtained from literature are consistent with the expected KPZ values of α = 1 / 2 , β = 1 / 3 , and z = 3 / 2 . A connection between the ballistic deposition and the KPZ equation through the limiting procedure and by applying the perturbation method was also presented.

Keywords

• universality class
• ballistic deposition model
• kpz equation
• finite-size scaling
• perturbation method