Renormalization-group transformation in a 2N-component fermionic hierarchical model

摘要

We study the 2N-component fermionic model of a hierarchical lattice and give explicit formulas for the renormalization-group transformation in the space of coefficients that determine a Grassmann-valued density of the free measure. We evaluate the inverse renormalization-group transformation. The definition of the renormalization-group fixed points reduces to a solution of a system of algebraic equations. We investigate solutions of this system for N = 1 2, 3. For alpha = 1; we prove an analogue of the central limit theorem for fermionic 2N-component fields. We discover all interesting relation between renormalization-group transformations in bosonic and fermionic hierarchical models and show, that one of these transformations is obtained from the other by replacing N with -N.