Impurity effects on domain-growth kinetics. I. Ising model

The development of order for the Ising model in the presence of static, random impurities is studied following a quench from high temperature (T{}Tc) to TTc. We find that for quenches to T=0, the system becomes pinned for long times for any value of c0 and never reaches its final equilibrium ferromagnetic ground state. The average linear pinned domain size scales as the inverse square root of the concentration c. For quenches to a final T0, the long-time behavior of the correlation length R and the energy E are slower than a power law, suggesting a logarithmic growth law for long times. The time that is required to reach this asymptotic logarithmic behavior increases as the impurity concentration decreases and/or the temperature increases.