Crossover and universality in the Wolf-Villain model.

The transition rules of the Wolf-Villain model for the deposition and instantaneous relaxation of particles on a lattice are expressed as a Langevin equation for the height fluctuations at each site. A coarse-graining transformation of this equation shows directly that this model belongs to the Edwards-Wilkinson universality class, in agreement with kinetic Monte Carlo simulations. The crossover from the Mullins-Herring equation is explained by the transformation under coarse graining of the coefficients in the equation of motion.