Dynamic renormalization group study of a generalized continuum model of crystalline surfaces

Abstract

We apply the Nozieres-Gallet dynamic renormalization group (RG) scheme to a continuum equilibrium model of a d-dimensional surface relaxing by linear surface tension and linear surface diffusion, and which is subject to a lattice potential favoring discrete values of the height variable. The model thus interpolates between the overdamped sine-Gordon model and a related continuum model of crystalline tensionless surfaces. The RG flow predicts the existence of an equilibrium roughening transition only for d = 2 dimensional surfaces, between a flat low-temperature phase and a rough high-temperature phase in the Edwards-Wilkinson (EW) universality class. The surface is always in the flat phase for any other substrate dimensions d > 2. For any value of d, the linear surface diffusion mechanism is an irrelevant perturbation of the linear surface tension mechanism, but may induce long crossovers within which the scaling properties of the linear molecular-beam epitaxy equation are observed, thus increasing the value of the sine-Gordon roughening temperature. This phenomenon originates in the non-linear lattice potential, and is seen to occur even in the absence of a bare surface tension term. An important consequence of this is that a crystalline tensionless surface is asymptotically described at high temperatures by the EW universality class.