KINETICS OF DOMAIN GROWTH IN FINITE ISING STRIPS

Monte Carlo simulations are presented for the kinetics of ordering of the two-dimensional nearest-neighbor Ising models in an L x M geometry with two free boundaries of length M much greater than L. This geometry models a "terrace" of width L on regularly stepped surfaces, adatoms adsorbed on neighboring terraces being assumed to be noninteracting. Starting out with an initially random configuration of the atoms in the lattice gas at coverage theta = 1/2 in the square lattice, quenching experiments to temperatures in the range 0.85 less-than-or-equal-to T/T(c) less-than-or-equal-to 1 are considered, assuming a dynamics of the Glauber model type (no conservation laws being operative). At T(c) the ordering behavior can be described in terms of a time-dependent correlation length xi(t), which grows with the time t after the quench as xi(t) approximately t1/z with the dynamic exponent z almost-equal-to 2.1, until the correlation length settles down at its equilibrium value 2L/pi (for correlations in the direction of the steps). Below T(c) a two-stage growth is observed: in the first stage, the scattering intensity [m2(t)BAR] grows linearly with time, as in the standard kinetic Ising model, until the domain size is of the same size as the terrace width. The further growth of [m2(t)BAR] in the second stage is consistent with a logarithmic law.