RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 TMF: Year: Volume: Issue: Page: Find

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

Critical dynamics as a field theory

N. V. Antonov, A. N. Vasil'ev

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.

Full text: PDF file (1455 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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
\Bibitem{AntVas84}
\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
\mathnet{http://mi.mathnet.ru/tmf5115}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 60
\issue 1
\pages 671--679
\crossref{https://doi.org/10.1007/BF01018251}

• http://mi.mathnet.ru/eng/tmf5115
• http://mi.mathnet.ru/eng/tmf/v60/i1/p59

 SHARE:

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. 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
2. Antonov, NV, “Field-theoretic renormalization group for a nonlinear diffusion equation”, Physical Review E, 66:4 (2002), 046105
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
4. Folk, R, “Critical dynamics: a field-theoretical approach”, Journal of Physics A-Mathematical and General, 39:24 (2006), R207
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
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
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
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
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
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
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
•  Number of views: This page: 503 Full text: 211 References: 43 First page: 3