Renormalization group study of Mullins’ equation for molecular beam epitaxy with conserved noise

Abstract

The dynamics of driven interfaces under conserved noise in a continuum model of growth by a molecular beam has been studied by means of the Noziéres–Gallet dynamic renormalization group technique, using the results of Sun and Plischke for the case of non-conserved noise. Relaxation of the growing film is due to both surface tension and surface diffusion. In (1+1) dimensions, four growth regimes have been found. None of these are purely diffusive. One of these fixed points has negative surface tension and is stable with respect to renormalization group flow. This is an unstable growth state in which the creation of large slopes in the interface configuration is expected. In (2+1) dimensions, seven growth regimes have been found, in which three are purely diffusive. There is also one fixed point with a negative surface tension. However, this fixed point is unstable with respect to renormalization group flow, and is therefore expected to crossover into the other growth regimes at large system size and long times.