Equilibrium roughening transition in a 1D modified sine-Gordon model

TL;DR

This paper introduces a modified 1D sine-Gordon model that exhibits a true thermodynamic roughening transition, providing analytical and numerical insights into phase behavior relevant to surface and wetting phenomena.

Contribution

The paper presents a novel 1D sine-Gordon model with a true phase transition, combining analytical transfer integral methods with Monte Carlo simulations for validation.

Findings

The model exhibits a phase transition between flat and rough phases.

Analytical transfer integral approach agrees with Monte Carlo results.

The model serves as an ideal framework for studying roughening transitions.

Abstract

We present a modified version of the one-dimensional sine-Gordon that exhibits a thermodynamic, roughening phase transition, in analogy with the 2D usual sine-Gordon model. The model is suited to study the crystalline growth over an impenetrable substrate and to describe the wetting transition of a liquid that forms layers. We use the transfer integral technique to write down the pseudo-Schr\"odinger equation for the model, which allows to obtain some analytical insight, and to compute numerically the free energy from the exact transfer operator. We compare the results with Monte Carlo simulations of the model, finding a perfect agreement between both procedures. We thus establish that the model shows a phase transition between a low temperature flat phase and a high temperature rough one. The fact that the model is one dimensional and that it has a true phase transition makes it an ideal framework for further studies of roughening phase transitions.