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We study the purely relaxational dynamics (model A) at criticality inthree-dimensional disordered Ising systems whose static critical behaviourbelongs to the randomly diluted Ising universality class. We consider thesite-diluted and bond-diluted Ising models, and the +- J Ising model along theparamagnetic-ferromagnetic transition line. We perform Monte Carlo simulationsat the critical point using the Metropolis algorithm and study the dynamicbehaviour in equilibrium at various values of the disorder parameter. Theresults provide a robust evidence of the existence of a unique model-A dynamicuniversality class which describes the relaxational critical dynamics in allconsidered models. In particular, the analysis of the size-dependence ofsuitably defined autocorrelation times at the critical point provides theestimate z=2.35(2) for the universal dynamic critical exponent. We also studythe off-equilibrium relaxational dynamics following a quench from T=\infty toT=T_c. In agreement with the field-theory scenario, the analysis of theoff-equilibrium dynamic critical behavior gives an estimate of z that isperfectly consistent with the equilibrium estimate z=2.35(2).

Relaxational dynamics in 3D randomly diluted Ising models