Renormalization-group methods for critical dynamics: II. Detailed analysis of the relaxational models

The relaxational models introduced in a previous treatment of critical dynamics are studied in detail using renormalization-group methods. The earlier results are justified by an analysis to all order in $\epsilon =4-d$, where $d$ is the dimensionality. The diagrammatic formalism of the full dynamic renormalization group is presented, and applied to the earlier models. A generalization of Wilson's Feynman-graph expansion method is used to calculate the exponents to second order in $\epsilon$. In model $C$, where a nonconserved order parameter is coupled to a conserved energy field, ambiguities were found in the earlier recursion-relation treatment for $2<n<\mathrm{}4\mathrm{}$, $d\approx 4$ ($n$ is the number of components of the order parameter). These ambiguities are discussed in the present work, but are not fully resolved.