Geodesic
The renormalization group transformation in the generalized fermionic hierarchical model
Izvestiya. Mathematics , Tome 87 (2023) no. 5, pp. 1011-1023

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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.
Keywords: renormalization group, hierarchical lattice, fermionic model, projective space. 
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M. D. Missarov; D. A. Khajrullin. The renormalization group transformation in the generalized fermionic hierarchical model. Izvestiya. Mathematics , Tome 87 (2023) no. 5, pp. 1011-1023. http://geodesic.mathdoc.fr/item/IM2_2023_87_5_a9/