Self-consistent calculation of statics and dynamics of the roughening transition

Statics and dynamics of the modified kinetic discrete Gaussian model are treated selfconsistently using a Gaussian probability assumption. A non-trivial roughening temperatureT _R is found in exactly two dimensions only. The free energyF, the correlation length and the interface roughness h ² are found to behave—lnFlnh ²(T _R –T)^–1 for temperaturesT approachingT _R from below. The linear relaxation rate of the order parameter is found to be proportional to ^–2. As a model for crystal growth, the growth rate depends linearly upon the chemical potential difference aboveT _R , shows a metastable regime belowT _R with a spinodal limit of metastability _c , beyond which oscillatory growth starts. The critical behavior of _c is found to be ln _c –(T _R –T)^–1+O(ln (T _R –T)).