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 expansion. In contrast to the situation in pure systems, the dynamic critical exponent z deviates from its conventional value at first order in 4-d. The impurities cause an enhancement of the shape function fₗ () at small frequencies ; fₗ (=0) diverges as TT₂. Below T₂ the equation of state, static susceptibility, 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), , 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.