On Critical Exponents and the Renormalization of the Coupling Constant in Growth Models with Surface Diffusion

TL;DR

This paper uses renormalized field theory to demonstrate that the coupling constant in growth models with surface diffusion undergoes nontrivial renormalization, leading to small but necessary corrections to the accepted scaling exponents.

Contribution

It provides a rigorous two-loop calculation showing the nontrivial renormalization of the coupling constant, challenging previous assumptions of invariance and exactness of scaling exponents.

Findings

Coupling constant renormalizes nontrivially in growth models with surface diffusion.

Corrections to scaling exponents are small but significant.

Accepted exponents are good approximations despite renormalization effects.

Abstract

It is shown by the method of renormalized field theory that in contrast to a statement based on a mathematically ill-defined invariance transformation and found in most of the recent publications on growth models with surface diffusion, the coupling constant of these models renormalizes nontrivially. This implies that the widely accepted supposedly exact scaling exponents are to be corrected. A two-loop calculation shows that the corrections are small and these exponents seem to be very good approximations.