Model of crystal growth with simulated self-attraction
  The (1+1)-dimensional kinetic model of crystal growth with simulated self-attraction and random sequential or parallel dynamics is introduced and studied via Monte-Carlo simulations. To imitate the attraction of absorbing atoms the probability of deposition is chosen to depend on the number of the nearest-neighbor atoms surrounding the deposited atom so it increases with this number. As well the evaporation probabilities are chosed to roughly account for this self-attraction. The model exhibits the interface depinning transition with KPZ-type roughness behavior in the moving phase. The critical indices of the correlation lengths are $\nu_\parallel = 0.82 \pm 0.03,{\rm{}}\nu_ \bot = 0.55 \pm 0.02$ and the critical index of the growth velocity is $1.08 \pm 0.03$ indicating the new universality class of the depinning transition. The critical properties of the model do not depend on the type of dynamics implemented. 
P. N. Timonin