Renormalization-group methods for critical dynamics: I. Recursion relations and effects of energy conservation

The renormalization-group method for studying critical phenomena is generalized to a class of dynamical systems—the time-dependent Ginzburg-Landau models. The effects of conservation laws on the critical dynamics are investigated through the study of models with different conservation properties for the energy and the space integral of the order parameter. Dynamic critical exponents near four dimensions ($d\approx 4$) are obtained from recursion relations, analogous to those of Wilson and Fisher. The physical significance of the time-dependent Ginzburg-Landau models is explored and the applicability of the results to experiments on the NMR linewidth of Fe${\mathrm{F}}_2$ is discussed.