Real-space dynamic renormalization group. III. Calculation of correlation functions

Abstract

The real-space dynamic renormalization group method developed in previous papers is applied to the kinetic Ising model defined on a square lattice. In particular we extend the formalism to the calculation of space- and time-dependent equilibrium averaged correlation functions. We find that conventional methods for implementing the real-space renormalization group via cumulant expansions in terms of the intercell coupling lead to correlation functions which decay algebraically in space at large distances in the disordered phase in qualitative disagreement with the known exponential decay. We indicate how one can develop new perturbation theory expansion methods which lead to the proper exponential decay at large distances and also lead to good quantitative results for other observable quantities like the magnetization, susceptibility, and single spin time autocorrelation function. As the result of a first-order calculation we obtain excellent results for the static critical exponents and a value of $z=1.79\mathrm{}$ for the dynamic critical exponent. The critical exponents obtained from the correlation functions calculated using this method satisfy the proper static and dynamic scaling relations.