Renormalization group in a fermionic hierarchical model in projective coordinates
Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 3, pp. 355-362 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the renormalization group action in a fermionic hierarchical model in the space of coefficients determining the Grassmann-valued density of the free measure. This space is interpreted as the two-dimensional projective space. The renormalization group map is a homogeneous quadratic map and has a special geometric property that allows describing invariant sets and the global dynamics in the whole space.
Keywords: fermionic model, hierarchical lattice, renormalization group, projective space, dynamics.
Mots-clés : invariant set
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M. D. Missarov. Renormalization group in a fermionic hierarchical model in projective coordinates. Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 3, pp. 355-362. http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a0/

[1] M. D. Missarov, “Renormalization group and renormalization theory in $p$-adic and adelic scalar models”, Dynamical Systems and Statistical Mechanics, Advances in Soviet Mathematics, 3, ed. Ya. G. Sinai, AMS, Providence, RI, 1991, 143–161 | MR

[2] V. S. Vladimirov, I. V. Volovich, E. I. Zelenov, $p$-Adicheskii analiz i matematicheskaya fizika, Fizmatlit, M., 1994 | MR | Zbl

[3] M. D. Missarov, TMF, 118:1 (1999), 40–50 | DOI | MR | Zbl

[4] É. Yu. Lerner, M. D. Missarov, J. Stat. Phys., 76:3–4 (1994), 805–817 | DOI | MR | Zbl

[5] E. Yu. Lerner, M. D. Missarov, TMF, 107:2 (1996), 201–212 | DOI | MR | Zbl

[6] M. D. Missarov, TMF, 114:3 (1998), 323–336 | DOI | MR | Zbl

[7] M. D. Missarov, TMF, 117:3 (1998), 471–488 | DOI | MR | Zbl

[8] M. D. Missarov, Phys. Lett. A, 253:1–2 (1999), 41–46 | DOI

[9] M. D. Missarov, “Renormalization group solution of fermionic Dyson model”, Asymptotic Combinatorics with Application to Mathematical Physics, Proceedings of the NATO Advanced Study Institute (St. Petersburg, Russia, July 9–22, 2001), NATO Science Series II: Mathematics, Physics and Chemistry, 77, eds. V. A. Malyshev, A. M. Vershik, Kluwer, Dordrecht, 2002, 151–166 | MR | Zbl