Geodesic
Asymptotic Behavior of Higher-Order Perturbations: Scaling Functions of the $O(n)$-Symmetric $\phi^4$-Theory in the $(4-\epsilon)$-Expansion
Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 3, pp. 387-402 
M. V. Komarova; M. Yu. Nalimov. Asymptotic Behavior of Higher-Order Perturbations: Scaling Functions of the $O(n)$-Symmetric $\phi^4$-Theory in the $(4-\epsilon)$-Expansion. Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 3, pp. 387-402. http://geodesic.mathdoc.fr/item/TMF_2001_129_3_a2/
@article{TMF_2001_129_3_a2,
     author = {M. V. Komarova and M. Yu. Nalimov},
     title = {Asymptotic {Behavior} of {Higher-Order} {Perturbations:} {Scaling} {Functions} of the $O(n)${-Symmetric} $\phi^4${-Theory} in the $(4-\epsilon)${-Expansion}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {387--402},
     year = {2001},
     volume = {129},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_129_3_a2/}
}
TY  - JOUR
AU  - M. V. Komarova
AU  - M. Yu. Nalimov
TI  - Asymptotic Behavior of Higher-Order Perturbations: Scaling Functions of the $O(n)$-Symmetric $\phi^4$-Theory in the $(4-\epsilon)$-Expansion
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2001
SP  - 387
EP  - 402
VL  - 129
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2001_129_3_a2/
LA  - ru
ID  - TMF_2001_129_3_a2
ER  - 
%0 Journal Article
%A M. V. Komarova
%A M. Yu. Nalimov
%T Asymptotic Behavior of Higher-Order Perturbations: Scaling Functions of the $O(n)$-Symmetric $\phi^4$-Theory in the $(4-\epsilon)$-Expansion
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2001
%P 387-402
%V 129
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2001_129_3_a2/
%G ru
%F TMF_2001_129_3_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

We use an instantonic approach to calculate the asymptotic behavior of higher orders of the $(4-\epsilon)$-expansion for the scaling function of the pair correlator of the $O(n)$-symmetric $\phi^4$-theory in the minimal subtraction scheme. Our results differ substantially from the known exact expression for the $\epsilon^3$ order of the expansion of the scaling function in the small-$\tau$ domain.

[1] L. N. Lipatov, ZhETF, 72 (1977), 411 | MR

[2] E. Brezin, J. C. Le Guillou, J. Zinn-Justin, Phys. Rev. D, 15 (1977), 1544 | DOI

[3] M. V. Komarova, M. Yu. Nalimov, TMF, 126:3 (2001), 409 | DOI | MR | Zbl

[4] J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, Oxford Univ. Press, Oxford, 1989 | MR

[5] A. N. Vasilev, Kvantovopolevaya renormgruppa v teorii kriticheskogo povedeniya i stokhasticheskoi dinamike, PIYaF, S-Pb., 1998

[6] M. Campostrini, A. Pelissetto, P. Rossi, E. Vicari, Phys. Rev. E, 57 (1998), 184 | DOI

[7] I. M. Suslov, ZhETF, 111 (1997), 220

[8] I. M. Suslov, ZhETF, 111 (1997), 1896

[9] V. G. Makhankov, Phys. Lett. A, 61 (1977), 431 | DOI

[10] A. J. Bray, Phys. Rev. B, 14 (1976), 1248 | DOI