Surface roughening in a hypercube-stacking model

We study in d+1 dimensions a new deposition and evaporation model of a d-dimensional surface which bears a Potts-spin representation. For the pure deposition case, our simulations on systems up to ${11520}^2$ sites in d=2 and 2×${192}^3$ sites in d=3 yield roughness exponents which violate recent conjectures. Including evaporation, we observe a nonequilibrium surface-roughening transition in d=3, but only a smooth crossover behavior in d=2. A logarithmic anomalous scaling form for surface width at the transition is conjectured.