Ordering kinetics in quasi-one-dimensional Ising-like systems

We present results of a Monte Carlo simulation of the kinetics of ordering in the two-dimensional nearest-neighbor Ising model in anL xM geometry with two free boundaries of length ML. This model can be viewed as representing an adsorbant on a stepped surface with mean terrace widthL. We follow the ordering kinetics after quenches to temperatures 0.25 T/T_c 1 starting from a random initial configuration at a coverage of=0.5 in the corresponding lattice gas picture. The systems evolve in time according to a Glauber kinetics with nonconserved order parameter. The equilibrium structure is given by a one-dimensional sequence of ordered domains. The ordering process evolves from a short initial two-dimensional ordering process through a crossover region to a quasi-one-dimensional behavior. The whole process is diffusive (inverse half-width of the structure factor peak 1/q_{¦¦ t}), in contrast to a model proposed by Kawasakiet al., where an intermediate logarithmic growth law is expected. All results are completely describable in the picture of an annihilating random walk (ARW) of domain walls.