Skip to main content
SpringerLink
Log in

Dynamics of renormalization group in the lower half-plane of the coupling constants of the fermionic hierarchical model

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We consider four-component fermionic (Grassmann-valued) field on the hierarchical lattice. The Gaussian part of the Hamiltonian in the model is invariant under the block-spin renormalization group transformation with given degree of normalization factor (renormalization group parameter). The non-Gaussian part of the Hamiltonian is given by the sum of the selfinteraction forms of the 2-nd and 4-th order. The action of the renormalization group transformation in this model is reduced to the rational map in the plane of coupling constants. We investigate the global dynamics of this map in the case when the coupling constant of the 4-th order form is less than zero (lower half-plane) and the renormalization group parameter belongs to the interval [1, 3/2).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Missarov, M. D. “RG-Invariant Curves in the Fermionic Hierarchical Model,” Theor. Math. Phys. 114, No. 3, 255–265 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  2. Missarov, M. D. “Critical Phenomena in the Fermionic Hierarchical Model,” Theor. Math. Phys. 117, No. 3, 1483–1498 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  3. Missarov, M. D. “Dynamical Phenomena in the Hierarchical Fermionic Model,” Phys. Lett. A253, 41–46 (1999).

    Google Scholar 

  4. Missarov, M. D. “Renormalization Group Solution of Fermionic Dyson Model,” in Asymptotic Combinatorics with Application to Mathematical Physics, Ed. by V. A. Malyshev and A. M. Vershik (Kluwer Academic Publishers, Netherlands, 2002), pp. 151–166.

    Google Scholar 

  5. Shamsutdinov, A. F. “Properties of Renormalization Group Flow in the Neighborhood of Gaussian Fixed Point,” Russian Mathematics (Iz. VUZ) 58, No. 9, 71–75 (2014).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    D. M. Missarov & A. F. Shamsutdinov

Authors
  1. D. M. Missarov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. F. Shamsutdinov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. M. Missarov.

Additional information

Original Russian Text © D.M. Missarov, A.F. Shamsutdinov, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 7, pp. 69–74.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Missarov, D.M., Shamsutdinov, A.F. Dynamics of renormalization group in the lower half-plane of the coupling constants of the fermionic hierarchical model. Russ Math. 59, 62–66 (2015). https://doi.org/10.3103/S1066369X15070087

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X15070087

Keywords

Search

Navigation