How (Super) Rough is the Glassy Phase of a Crystalline Surface with a Disordered Substrate?

TL;DR

This paper investigates the potential existence of a super-rough glassy phase in a crystalline surface with a disordered substrate, using numerical simulations to demonstrate its presence and discussing theoretical approaches to explain it.

Contribution

The study provides numerical evidence for a super-rough glassy phase in crystalline surfaces with disorder, highlighting the need for advanced theoretical methods.

Findings

Identification of super-rough behavior with height correlations as square logarithm of distance

Numerical simulations confirm the phase is not due to finite size effects

Discussion on the limitations of current variational approaches

Abstract

We discuss the behavior of a crystalline surface with a disordered substrate. We focus on the possible existence of a {\em super-rough} glassy phase, with height-height correlation functions which vary as the square logarithm of the distance. With numerical simulations we establish the presence of such a behavior, that does not seem to be connected to finite size effects. We comment on the variational approach, and suggest that a more general extension of the method could be needed to explain fully the behavior of the model.