Coarse-graining a restricted solid-on-solid model

TL;DR

This paper applies a coarse-graining procedure to a restricted solid-on-solid model with adsorption and desorption, deriving continuum equations that match simulations and exhibit known universality class exponents.

Contribution

It demonstrates a systematic method to derive continuum equations from discrete solid-on-solid models, confirming the universality class behavior and coefficient stability.

Findings

Continuum equations agree with direct simulations.

Model exhibits Edwards-Wilkinson or KPZ exponents.

Coefficients remain well-defined in the coarse-grained limit.

Abstract

A procedure suggested by Vvedensky for obtaining continuum equations as the coarse-grained limit of discrete models is applied to the restricted solid-on-solid model with both adsorption and desorption. Using an expansion of the master equation, discrete Langevin equations are derived; these agree quantitatively with direct simulation of the model. From these, a continuum differential equation is derived, and the model is found to exhibit either Edwards-Wilkinson or Kardar-Parisi-Zhang exponents, as expected from symmetry arguments. The coefficients of the resulting continuum equation remain well-defined in the coarse-grained limit.