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TMF, 1984, Volume 60, Number 1, Pages 59–71 (Mi tmf5115)  

This article is cited in 11 scientific papers (total in 11 papers)

Critical dynamics as a field theory

N. V. Antonov, A. N. Vasil'ev

Leningrad State University

Abstract: Critical dynamics [1-3] is considered systematically from the point of view of quantum field theory. The connection between dynamics and statics and its consequences for the renormalization constants is discussed in detail. The main technical result is the 3 calculation of the $\varepsilon^3$ contribution in the $4-2\varepsilon$ expansion of the dynamical exponent $\Delta_\omega$ (critical dimension of frequency) for the $O_n$-symmetrie $\varphi^4$ model. Instead of the value $\Delta_\omega=2+0,726(1-2\varepsilon\cdot 1,687)\eta$ obtained previously [4], the value $\Delta_\omega=2+0,726(1-2\varepsilon\cdot 0,1885)\eta$ is obtained.

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English version:
Theoretical and Mathematical Physics, 1984, 60:1, 671–679

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Received: 20.07.1983

Citation: N. V. Antonov, A. N. Vasil'ev, “Critical dynamics as a field theory”, TMF, 60:1 (1984), 59–71; Theoret. and Math. Phys., 60:1 (1984), 671–679

Citation in format AMSBIB
\by N.~V.~Antonov, A.~N.~Vasil'ev
\paper Critical dynamics as a field theory
\jour TMF
\yr 1984
\vol 60
\issue 1
\pages 59--71
\jour Theoret. and Math. Phys.
\yr 1984
\vol 60
\issue 1
\pages 671--679

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    This publication is cited in the following articles:
    1. L. Ts. Adzhemyan, A. N. Vasil'ev, M. Gnatich, Yu. M. Pis'mak, “Quantum field renormalization group in the theory of stochastic Langmuir turbulence”, Theoret. and Math. Phys., 78:3 (1989), 260–271  mathnet  crossref  mathscinet  isi
    2. Antonov, NV, “Field-theoretic renormalization group for a nonlinear diffusion equation”, Physical Review E, 66:4 (2002), 046105  crossref  isi
    3. A. S. Krinitsyn, V. V. Prudnikov, P. V. Prudnikov, “Calculations of the dynamical critical exponent using the asymptotic series summation method”, Theoret. and Math. Phys., 147:1 (2006), 561–575  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Folk, R, “Critical dynamics: a field-theoretical approach”, Journal of Physics A-Mathematical and General, 39:24 (2006), R207  crossref  isi
    5. Fan, SL, “Determination of the dynamic and static critical exponents of the two-dimensional three-state Potts model using linearly varying temperature”, Physical Review E, 76:4 (2007), 041141  crossref  adsnasa  isi
    6. Prudnikov, VV, “Renormalization-group description of nonequilibrium critical short-time relaxation processes: A three-loop approximation”, Journal of Experimental and Theoretical Physics, 106:6 (2008), 1095  crossref  adsnasa  isi
    7. L. Ts. Adzhemyan, M. V. Kompaniets, “Renormalization group and the $\varepsilon$-expansion: Representation of the $\beta$-function and anomalous dimensions by nonsingular integrals”, Theoret. and Math. Phys., 169:1 (2011), 1450–1459  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    8. L. Ts. Adzhemyan, S. E. Vorobyeva, M. V. Kompaniets, “Representation of the $\beta$-function and anomalous dimensions by nonsingular integrals in models of critical dynamics”, Theoret. and Math. Phys., 185:1 (2015), 1361–1369  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. Adzhemyan L.Ts. Ivanova E.V. Kompaniets M.V. Vorobyeva S.Y., “Diagram Reduction in Problem of Critical Dynamics of Ferromagnets: 4-Loop Approximation”, J. Phys. A-Math. Theor., 51:15 (2018), 155003  crossref  isi
    10. L. Ts. Adzhemyan, S. E. Vorob'eva, E. V. Ivanova, M. V. Kompaniets, “Representation of renormalization group functions by nonsingular integrals in a model of the critical dynamics of ferromagnets: The fourth order of the $\varepsilon$-expansion”, Theoret. and Math. Phys., 195:1 (2018), 584–594  mathnet  crossref  crossref  adsnasa  isi  elib
    11. Hnatic M. Kalagov G. Lucivjansky T., “Scaling Behavior in Interacting Systems: Joint Effect of Anisotropy and Compressibility”, Eur. Phys. J. B, 91:11 (2018), 269  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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