Directed d-mer diffusion describing the Kardar-Parisi-Zhang surface growth

We show that d+1-dimensional surface growth models can be mapped onto driven lattice gases of d-mers. The Kardar-Parisi-Zhang growth corresponds to one dimensional drift of d-mers perpendicular to the (d − 1)-dimensional ”plane” spanned by the d-mers. This facilitates efficient, bit-coded algorithms with generalized Kawasaki dynamics of spins. Our simulations in d = 2, 3, 4, 5 dimensions provide scaling exponent estimates on much larger system sizes and simulations times published so far, where the effective growth exponent exhibits an increase. We provide evidence for the agreement of some field theoretical predictions and numerics. We show that the (2 + 1)-dimensional exponents conciliate with the values suggested by L¨assig within error margin. The increase of the effective growth exponents suggest a crossover to a different, anisotropic scaling behavior in d = 5 dimensions.