Renormalization group transformation in the generalized fermionic hierarchical model
- Authors: Missarov M.D.1, Khajrullin D.A.1
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Affiliations:
- Kazan (Volga Region) Federal University
- Issue: Vol 87, No 5 (2023)
- Pages: 164-176
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/140435
- DOI: https://doi.org/10.4213/im9371
- ID: 140435
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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 adjacent vertices and is, in fact, 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 transformation of the renormalization group. The transformation of the renormalization group in the space of coefficients that determine the Grassmann-valued density of the free measure is calculated explicitly as a homogeneous mapping of the fourth degree in a two-dimensional projective space. The properties of this mapping are described.
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About the authors
Mukadas Dmukhtasibovich Missarov
Kazan (Volga Region) Federal University
Email: Moukadas.Missarov@kpfu.ru
Doctor of physico-mathematical sciences, Professor
Dmitrii Airatovich Khajrullin
Kazan (Volga Region) Federal University
Email: dimahajrullin@outlook.com
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