Critical dynamics and renormalization-group methods for the kinetic Ising model

The theory of the critical dynamics of the single spin-flip kinetic Ising model is examined. Various unproven assumptions and misconceptions are uncovered and discussed. In particular, we point out that the condition of detailed balance places important constraints on the renormalization-group analysis of this problem. The relationship among different fixed-point dynamical operators and dynamic universality classes is clarified. The role and convergence of perturbation-theory expansions which treat the bare coupling between cells as a small parameter in the real-space renormalization-group treatment are analyzed. We give reasons for believing that this approach cannot compete with methods using direct high-temperature expansions. We also comment on the usefulness of other methods in treating this problem.