Dynamics of spins interacting with quenched random impurities

The critical dynamics of the time-dependent Ginzburg-Landau model for a system with quenched random impurities and nonconserved order parameter is studied in the framework of the ε expansion. In contrast to the situation in pure systems, the dynamic critical exponent z deviates from its conventional value at first order in ε≡4-d. The impurities cause an enhancement of the shape function fₓ(ν) at small frequencies ν; fₓ(ν=0) diverges as T→Tc. Below Tc the equation of state, static susceptibility χ, and dynamic response function G, are studied. A new, purely static correlated function, C⁽ˢ⁾, whose existence is unique to the random system is introduced. The coexistence curve singularities of C⁽ˢ⁾, χ, and G in systems with continuously broken symmetry are explored. The connection of the quenched-impurity model with "model C" of Halperin, Hohenberg, and Ma is discussed.