Dynamical renormalization of kinetic van der Waals spin models

An exact dynamical renormalization approach in differential form is proposed for kinetic van der Waals spin systems with general many-body interactions. The problem of restoring covariance in the evolution equation after renormalization of the model is solved by introducing a suitable renormalized time parameter, which depends also on the magnetization of the spin configuration. The study of the behavior of this renormalized time near criticality leads to a scaling relation for the linear relaxation time. This relation can be shown to imply the exact results for the dynamical critical behavior of the system