This article is cited in 6 papers

Renormalization group in a fermionic hierarchical model

É. Yu. Lerner, M. D. Missarov

Kazan State University

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.

Received: 27.10.1993

 English version: Theoretical and Mathematical Physics, 1994, 101:2, 1353–1360

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