Apparent phase transitions in finite one-dimensional sine-Gordon lattices

TL;DR

This paper investigates apparent phase transitions in finite one-dimensional sine-Gordon lattices, explaining their occurrence through transfer operator formalism despite the absence of true phase transitions in the infinite system.

Contribution

It provides a theoretical explanation for the observed finite-size effects and apparent phase transitions in the sine-Gordon model using transfer operator analysis.

Findings

Finite lattices show apparent phase transitions at high temperatures.

Transfer operator formalism explains the finite-size effects.

No true phase transition exists in the infinite system.

Abstract

We study the one-dimensional sine-Gordon model as a prototype of roughening phenomena. In spite of the fact that it has been recently proven that this model can not have any phase transition [J. A. Cuesta and A. Sanchez, J. Phys. A 35, 2373 (2002)], Langevin as well as Monte Carlo simulations strongly suggest the existence of a finite temperature separating a flat from a rough phase. We explain this result by means of the transfer operator formalism and show as a consequence that sine-Gordon lattices of any practically achievable size will exhibit this apparent phase transition at unexpectedly large temperatures.