Abstract
We consider a two-dimensional hierarchical lattice in which the vertices of a square represent an elementary cell. In the generalized hierarchical model, the distance between opposite vertices of a square differs from that between adjacent vertices and is a parameter of the new model. The Gaussian part of the Hamiltonian of the 4-component generalized fermionic hierarchical model is invariant under the block-spin renormalization group transformation. The transformation of the renormalization group in the space of coefficients, which specify the Grassmann-valued density of the free measure, is explicitly calculated as a homogeneous mapping of degree four in the two-dimensional projective space.
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