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 T < Tc. We find that for quenches to T = 0, the system becomes pinned for long times for any value of c > 0 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 T > 0, 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.