Analytic study of domain growth in the Ising model with quenched impurities

Abstract

We analytically study the one-dimensional kinetic Ising model with Glauber dynamics in the presence of quenched impurities. We derive the evolution equations for the expectation value of spin and the equal-time pair correlation function. The scaling form of the structure factor is given by ${\mathrm{G}}_{\mathrm{k}}$(t)=(1-\ensuremath{\rho})${\mathrm{t}}^{1\mathrm{/}2}$g((1-${\mathrm{\ensuremath{\rho}}}^{2}$)${\mathrm{k}}^{2}$t,${\mathrm{\ensuremath{\rho}}}^{2}$t) with the impurity concentration \ensuremath{\rho}, and its scaling function is calculated at zero temperature. We also obtain the average pinned domain size at long time for quenches to T=0 in one dimension, and find that it scales inversely with impurity concentration for the small \ensuremath{\rho}.