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TMF, 2006, Volume 146, Number 3, Pages 365–384 (Mi tmf2041)  

This article is cited in 3 scientific papers (total in 3 papers)

Epsilon-expansion in the $N$-component $\varphi^4$ model

M. D. Missarov, R. G. Stepanov

Kazan State University

Abstract: The formalism of projection Hamiltonians is applied to the $N$-component $O(N)$-invariant $\varphi^4$ model in the Euclidean and $p$-adic spaces. We use two versions of the $\varepsilon$-expansion (with $\varepsilon=4-d$ and $\varepsilon=\alpha-3d/2$ where $\alpha$ is the renormalization group parameter) and evaluate the critical indices $\nu$ and $\eta$ up to the second order of the perturbation theory. The results for the $(4-d)$-expansion then coincide with the known results obtained via the quantum-field renormalization-group methods. Our calculations give evidence that in dimension three, both expansions describe the same non-Gaussian fixed point of the renormalization group.

Keywords: $\varepsilon$-expansion, renormalization group, Euclidean models, $p$-adic models, perturbation theory, critical indices.

DOI: https://doi.org/10.4213/tmf2041

Full text: PDF file (257 kB)
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English version:
Theoretical and Mathematical Physics, 2006, 146:3, 304–320

Bibliographic databases:

Received: 07.04.2005
Revised: 06.06.2005

Citation: M. D. Missarov, R. G. Stepanov, “Epsilon-expansion in the $N$-component $\varphi^4$ model”, TMF, 146:3 (2006), 365–384; Theoret. and Math. Phys., 146:3 (2006), 304–320

Citation in format AMSBIB
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\by M.~D.~Missarov, R.~G.~Stepanov
\paper Epsilon-expansion in the $N$-component $\varphi^4$ model
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\pages 365--384
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\jour Theoret. and Math. Phys.
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\issue 3
\pages 304--320
\crossref{https://doi.org/10.1007/s11232-006-0041-5}
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  • http://mi.mathnet.ru/eng/tmf/v146/i3/p365

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Proc. Steklov Inst. Math., 265 (2009), 229–234  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. Gubser S.S. Parikh S., “Geodesic Bulk Diagrams on the Bruhat-Tits Tree”, Phys. Rev. D, 96:6 (2017), 066024  crossref  mathscinet  isi  scopus  scopus
    3. Gubser S.S. Jepsen Ch. Parikh S. Trundy B., “O(N) and O(N) and O(N)”, J. High Energy Phys., 2017, no. 11, 107  crossref  mathscinet  zmath  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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