Higher-order calculations in the real space dynamic renormalization group: One dimension

The application of real space dynamic renormalization group methods to the one-dimensional kinetic Ising model, discussed in an earlier paper, is extended to one order higher in perturbation theory than was done previously. It is shown that the treatment of short-range, local quantities is improved in going to higher order in the perturbation expansion, while that of the long-range properties remains largely unaffected. Arbitrariness in the real space mapping function and how it may be exploited to our advantage is duscussed. It is shown that the renormalized Hamiltonian continues to be characterized by one coupling through second order. We find that the single spin-flip kinetic Ising model generates at second-order new spin-flip mechanisms in the renormalized dynamical operator but that their effects are small (at most 2%) over the entire temperature range.