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

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-Schrödinger 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.

11 pages, 13 figures. Accepted for publication in Physical Review E

References in corpus (3)

• General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
• Thermodynamic instabilities in one dimensional particle lattices: a finite-size scaling approach
• Super-roughening as a disorder-dominated flat phase

Cited by in corpus (5)

• Probability distribution of bubble lengths in DNA
• Dependence on temperature and GC content of bubble length distributions in DNA
• Modelling Disorder: the Cases of Wetting and DNA Denaturation
• Numerical Simulations of Random Phase Sine-Gordon Model and Renormalization Group Predictions
• On the Pseudo-Schrödinger Equation approximation of the Transfer-Integral operator for 1-dimensional DNA models