Transformation of the renormalization group in generalized fermionic hierarchical model

We consider a two-dimensional hierarchical lattice, 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 adjacent vertices and is, in fact, a new parameter of the model. The Gaussian part of the Hamiltonian of the 4-component generalized fermionic hierarchical model is invariant under the block-spin transformation with a given value of the renormalization group parameter. The Grassmann-valued density of the free measure in this model is described as the sum of forms of the 2nd and 4th degrees. The transformation of the renormalization group in the space of the coefficients of this density is calculated explicitly as a homogeneous mapping of the fourth degree in a two-dimensional projective space. The properties of this mapping are described.