Single tensionless transition in the Laplacian roughening model

TL;DR

This study uses large-scale Monte Carlo simulations to investigate the discrete Laplacian roughening model, revealing a single, possibly Kosterlitz-Thouless, phase transition between flat and rough phases, challenging previous beliefs about multiple transitions.

Contribution

It provides the first large-scale simulation evidence for a single tensionless transition in the dLr model, clarifying its phase diagram and the nature of the transition.

Findings

Identifies a single phase transition in the dLr model.

Suggests the transition is of the Kosterlitz-Thouless type.

Challenges earlier claims of multiple transitions and a hexatic phase.

Abstract

We report large scale Monte Carlo simulations of the equilibrium discrete Laplacian roughening (dLr) model, originally introduced as the simplest one accommodating the hexatic phase in two-dimensional melting. The dLr model is also relevant to surface roughening in molecular beam epitaxy (MBE). Our data suggest a single phase transition, possibly of the Kosterlitz-Thouless type, between a flat low-temperature phase and a rough, tensionless, high-temperature phase. Thus, earlier conclusions on the order of the phase transition and on the existence of a hexatic phase are seen as due to finite size effects, the phase diagram of the dLr model being similar to that of a continuum analog previously formulated in the context of surface growth by MBE.