Elementary local configurations, microscopic rules and Langevin equations for two models of molecular-beam epitaxy

Abstract

Stochastic Langevin equations for the Wolf-Villain (WV) and Das Sarma-Tamborenea (DT) models are derived using the alternative method recently developed by Costanza (1997 Phys. Rev. E 55 6501) which avoids the complications arising in the calculation of the first moment of the transition rate required in the master equation approach. The calculations are compared with those recently published by Zhi-Feng Huang et al (1996 Phys. Rev. E 54 5935) obtaining the same results, as is expected. The microscopic rules are derived from the set of 243 elementary local configurations needed for the description of these two models and after using simple summation rules these were reduced to 16 for the DT model and to 25 for the WV model. The number of microscopic rules needed for the description of the present models are considerably larger than the previously solved models.