Radial Restricted Solid-on-Solid and Etching Interface Growth Models

TL;DR

This paper introduces a method to generate radial interfaces for growth models, verifying the KPZ conjecture and showing strong agreement with theoretical distributions and correlations, enabling studies of radial interface evolution.

Contribution

It presents a novel recursive radial network approach to adapt flat substrate models for radial interface growth, confirming universality class predictions.

Findings

KPZ conjecture fully verified for radial models

Interface radius fluctuation matches GUE distribution

Two-point correlation aligns with Airy$_2$ covariance

Abstract

In this work, an approach to generate radial interfaces is presented. A radial network recursively obtained is used to implement discrete model rules designed originally for the investigation in flat substrates. In order to test the proposed scheme, we have used the restricted solid-on-solid and etching models. The results indicate the KPZ conjecture is fully verified. Besides, a very good agreement between the interface radius fluctuation distribution and the GUE one was observed. The evolution of the radius agrees very well with the generalized conjecture, and the two-point correlation function exhibits a very good agreement with the covariance of Airy$_2$ process. So, this approach can be used to investigate radial interfaces evolution for others universality classes.