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Renormalization group in a fermionic hierarchical model

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Abstract

A study is made of a hierarchical model with spin values in a Grassmann algebra defined by a potential of general form. The action of the spin-block renormalization group in the space of Hamiltonians is reduced to a rational mapping of the space of coupling constants into itself. The methods of the theory of bifurcations are used to investigate the nontrivial fixed points of this mapping. A theorem establishing the existence of a thermodynamic limit of the model at these points in a certain neighborhood of a bifurcation value is proved.

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Authors
  1. É. Yu. Lerner
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  2. M. D. Missarov
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Additional information

This work was done with financial support of the Russian Foundation for Fundamental Research (Grant 93-011-16099).

State University, Kazan. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 101, No. 2, pp. 282–293, November, 1994.

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Lerner, É.Y., Missarov, M.D. Renormalization group in a fermionic hierarchical model. Theor Math Phys 101, 1353–1360 (1994). https://doi.org/10.1007/BF01018283

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  • DOI: https://doi.org/10.1007/BF01018283

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