Dynamical universality classes of simple growth and lattice gas models
Abstract
Large scale, dynamical simulations have been performed for the two dimensional octahedron model, describing the KardarParisiZhang (KPZ) for nonlinear, or the EdwardsWilkinson class for linear surface growth. The autocorrelation functions of the heights and the dimer lattice gas variables are determined with high precision. Parallel randomsequential (RS) and twosublattice stochastic dynamics (SCA) have been compared. The latter causes a constant correlation in the long time limit, but after subtracting it one can find the same height functions as in case of RS. On the other hand the ordered update alters the dynamics of the lattice gas variables, by increasing (decreasing) the memory effects for nonlinear (linear) models with respect to RS. Additionally, we support the KPZ ansatz and the KallabisKrug conjecture in 2+1 dimensions and provide a precise growth exponent value β={0.2414}(2) . We show the emergence of finite size corrections, which occur long before the steady state roughness is reached.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 January 2018
 DOI:
 10.1088/17518121/aa97f3
 arXiv:
 arXiv:1701.03638
 Bibcode:
 2018JPhA...51c5003K
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Materials Science;
 Nonlinear Sciences  Cellular Automata and Lattice Gases;
 Physics  Computational Physics
 EPrint:
 26 pages, 22 figures (counting subfigures)