Vertically extended Frenkel-Kontorova model: a real space renormalization group study

TL;DR

This paper introduces a vertically extended Frenkel-Kontorova model to analyze island formation and roughness transitions in monolayer 1D interfaces, utilizing analytical and real space renormalization group methods.

Contribution

It extends the classical Frenkel-Kontorova model by allowing vertical particle movement, providing new insights into interface roughness and island formation.

Findings

Identifies conditions for island formation.

Characterizes roughness transition behavior.

Demonstrates effectiveness of real space RG techniques.

Abstract

A modification of the Frenkel-Kontorova model is presented in which particles are allowed to move in the vertical direction. This model is used to study the formation of islands for a monolayer of 1D interfaces and the corresponding roughness transition. Both analytical and numerical approaches are employed, and the numerical algorithm is based upon real space renormalization group techniques.