Kinetics of domain growth in finite Ising strips

Abstract

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 = 1 2 in the square lattice, quenching experiments to temperatures in the range 0.85⩽ T/ T c⩽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 ξ( t), which grows with the time t after the quench as ξ(t)∼t 1 z with the dynamic exponent z≈2.1, until the correlation length settles down at its equilibrium value 2 L/π (for correlations in the direction of the steps). Below T c a two-stage growth is observed: in the first stage, the scattering intensity 〈 m 2( 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 〈 m 2( t)〉 in the second stage is consistent with a logarithmic law.