Nonequilibrium critical relaxation in the presence of random impurities.

Abstract

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)=[〈\ensuremath{\partial}${\mathrm{\ensuremath{\varphi}}}_{\mathbf{k}}$(t)/\ensuremath{\partial}${\mathrm{\ensuremath{\varphi}}}_{\mathrm{\ensuremath{-}}\mathbf{k}}$(0)〉] and the structure factor ${\mathit{S}}_{\mathit{k}}$(t)=[〈${\mathrm{\ensuremath{\varphi}}}_{\mathbf{k}}$(t)${\mathrm{\ensuremath{\varphi}}}_{\mathrm{\ensuremath{-}}\mathbf{k}}$(t)〉] are calculated to first order in \ensuremath{\epsilon} (\ensuremath{\epsilon}=4-d) for the O(n) model. For a nonconserved order parameter, the scaling form ${\mathit{G}}_{\mathit{k}}$(t)=${\mathit{t}}^{\ensuremath{\lambda}/\mathit{z}}$f(${\mathit{k}}^{\mathit{z}}$t) is obtained, with f(0)=const and \ensuremath{\lambda}=\ensuremath{\epsilon}/4+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$), for 1n4. For n>4, random impurities are irrelevant, and \ensuremath{\lambda}=[(n+2)/2(n+8)]\ensuremath{\epsilon}+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$), in agreement with calculations on the pure system. For a conserved order parameter \ensuremath{\lambda}=0, but the scaling function f(x) is nontrivial. For both conserved and nonconserved order parameter, disorder gives rise to algebraically decaying scaling functions.