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 ⪢ 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 θ = 12 in the square lattice, quenching experiments to temperatures in the range 0.85⩽T/Tc⩽1 are considered, assuming a dynamics of the Glauber model type (no conservation laws being operative). At Tc the ordering behavior can be described in terms of a time-dependent correlation length ξ(t), which grows with the time t after the quench as ξ(t)∼t1z with the dynamic exponent z≈2.1, until the correlation length settles down at its equilibrium value 2L/π (for correlations in the direction of the steps). Below Tc a two-stage growth is observed: in the first stage, the scattering intensity 〈m2(t)〉 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)〉 in the second stage is consistent with a logarithmic law.