Fixed points of transformation of a renormalization group in a generalized fermionic hierarchical model

Abstract

A two-dimensional hierarchical lattice is considered, in which an elementary cell is represented by the vertices of a square. In the generalized hierarchical model, the distance between opposite vertices of a square differs from the distance between neighboring vertices and is a parameter of the new model. At each vertex of the lattice, the field is defined by a set of 4 generators of the Grassmann algebra. The Hamiltonian of the field is described by the interaction of the 4th degree. The transformation of the renormalization group in the space of coupling coefficients defining this interaction is defined as a nonlinear mapping. All branches of fixed points of this mapping are described.