Equivalence of the Wilson and Wegner-Houghton generators to first order in perturbation theory at arbitrary anisotropic fixed points

Abstract

We extend our proof of the equivalence of the Wilson and Wegner-Houghton generators (previously given for isotropic fixed points and to first order in a perturbation expansion for the critical exponents) to all fixed points which can be described by the corresponding approximate generators. This includes all those fixed points which are to leading order "wave-vector independent." The proof is again to first order in perturbation theory and exploits the properties of the linearized eigenfunctions (eigenoperators) to evaluate the nonlinear terms.