Eur. Phys. J. B 14, 713-724 (2000)
https://doi.org/10.1007/s100510051083

Functional renormalization description of the roughening transition

¹ Service de Physique de l'État Condensé, Centre d'Études de Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France
² Laboratoire de Physique Théorique de l'École Normale SupérieureUnité propre du CNRS, associée à l'École Normale Supérieure et à l'Université Paris-Sud, 24 rue Lhomond, 75231 Paris Cedex 05, France

Received: 16 April 1999
Revised: 11 October 1999
Published online: 15 April 2000

Abstract

We reconsider the problem of the static thermal roughening of an elastic manifold at the critical dimension d=2 in a periodic potential, using a perturbative Functional Renormalization Group approach. Our aim is to describe the effective potential seen by the manifold below the roughening temperature on large length scales. We obtain analytically a flow equation for the potential and surface tension of the manifold, valid for low temperatures. On a length scale L, the renormalized potential is made up of a succession of quasi parabolic wells, matching onto one another in a singular region of width ~ L^-6/5 for large L. For strong periodic potential, the perturbation theory breaks down, and we argue, based on a variational calculation, that the transition becomes first order. We also obtain numerically the step energy as a function of temperature, and relate our results to the existing experimental data on ⁴He. Finally, we examine the case of a non local elasticity which is realized physically for the contact line.