Glassy Roughness of a Crystalline Surface Upon a Disordered Substrate

TL;DR

This study uses Monte Carlo simulations to explore how a crystalline surface's roughness transitions from thermal to disorder-driven glassy behavior when deposited on a disordered substrate, revealing a phase transition and contrasting theoretical predictions.

Contribution

It demonstrates a continuous transition to a glassy roughness phase and compares the results with various theoretical approaches, highlighting discrepancies with renormalization group predictions.

Findings

Identifies a phase transition from thermal to glassy roughness.

Height correlations align with one-step replica symmetry breaking.

Results differ from renormalization group and vortex-glass simulations.

Abstract

The discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is studied by Monte Carlo simulations. A continuous transition is found from a phase with a thermally-induced roughness to a glassy one in which the roughness is driven by the disorder. The behavior of the height-height correlations is consistent with the one-step replica symmetry broken solution of the variational approximation. The results differ from the renormalization group predictions and from recent simulations of a 2D vortex-glass model which belongs to the same universality class.