Nonequilibrium critical relaxation in the presence of random impurities

The effect of random impurities (quenched disorder) on the growth of correlations is studied for model A and model B after a sudden quench to ${\mathit{T}}_{\mathit{c}}$ from the high-temperature phase (i.e., random initial conditions). Exponents and scaling functions of the nonequilibrium dynamic response function ${\mathit{G}}_{\mathit{k}}$(t)=[〈∂${\mathrm{\phi }}_{\mathbf{k}}$(t)/∂${\mathrm{\phi }}_{\mathrm{-}\mathbf{k}}$(0)〉] and the structure factor ${\mathit{S}}_{\mathit{k}}$(t)=[〈${\mathrm{\phi }}_{\mathbf{k}}$(t)${\mathrm{\phi }}_{\mathrm{-}\mathbf{k}}$(t)〉] are calculated to first order in ε (ε=4-d) for the O(n) model. For a nonconserved order parameter, the scaling form ${\mathit{G}}_{\mathit{k}}$(t)=${\mathit{t}}^{\lambda /\mathit{z}}$f(${\mathit{k}}^{\mathit{z}}$t) is obtained, with f(0)=const and λ=ε/4+O(${\mathrm{\epsilon }}^2$), for 1<n<4. For n>4, random impurities are irrelevant, and λ=[(n+2)/2(n+8)]ε+O(${\mathrm{\epsilon }}^2$), in agreement with calculations on the pure system. For a conserved order parameter λ=0, but the scaling function f(x) is nontrivial. For both conserved and nonconserved order parameter, disorder gives rise to algebraically decaying scaling functions.