Equilibrium roughening transition in a one-dimensional modified sine-Gordon model

Abstract

We present a modified version of the one-dimensional sine-Gordon model that exhibits a thermodynamic, roughening phase transition, in analogy with the two-dimensional 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-Schrödinger equation for the model, which allows us 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 with intriguing nontrivial properties 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.