Geodesic
Calculation of the critical index $\eta$ for the $\varphi^3$ theory by the conformal bootstrap method
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 179-185 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We propose a method for calculating the $\epsilon$-expansion in the model of a scalar field with the $\varphi^3$ interaction based on the conformal bootstrap equations. We calculate the index $\eta$ in the three-loop approximation. Our result coincides with the result previously obtained by the method of renormalization group equations based on calculating a large number of Feynman diagrams.
Keywords: conformal bootstrap, $\varphi^3$ theory, critical index. 
@article{TMF_2015_185_1_a15,
     author = {A. L. Pismenskii},
     title = {Calculation of the~critical index $\eta$ for the~$\varphi^3$ theory by the~conformal bootstrap method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {179--185},
     year = {2015},
     volume = {185},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a15/}
}
TY  - JOUR
AU  - A. L. Pismenskii
TI  - Calculation of the critical index $\eta$ for the $\varphi^3$ theory by the conformal bootstrap method
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2015
SP  - 179
EP  - 185
VL  - 185
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a15/
LA  - ru
ID  - TMF_2015_185_1_a15
ER  - 
%0 Journal Article
%A A. L. Pismenskii
%T Calculation of the critical index $\eta$ for the $\varphi^3$ theory by the conformal bootstrap method
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2015
%P 179-185
%V 185
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a15/
%G ru
%F TMF_2015_185_1_a15
A. L. Pismenskii. Calculation of the critical index $\eta$ for the $\varphi^3$ theory by the conformal bootstrap method. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 179-185. http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a15/

[1] A. N. Vasilev, Kvantovopolevaya renormgruppa v teorii kriticheskogo povedeniya i stokhasticheskoi dinamike, PIYaF, SPb., 1998 | MR

[2] A. N. Vasilev, Yu. M. Pismak, Yu. R. Khonkonen, TMF, 46:2 (1981), 157–171 | DOI | MR

[3] A. N. Vasilev, Yu. M. Pismak, Yu. R. Khonkonen, TMF, 47:3 (1981), 291–306 | DOI

[4] A. N. Vasilev, Yu. M. Pismak, Yu. R. Khonkonen, TMF, 50:2 (1982), 195–206 | DOI

[5] T. Huber, D. Maître, Comput. Phys. Commun., 178:10 (2008), 755–776, arXiv: 0708.2443 | DOI | MR | Zbl

[6] D. I. Kazakov, TMF, 62:1 (1985), 127–135 | DOI

[7] P. A. Baikov, K. G. Chetyrkin, Nucl. Phys. B, 837:3 (2010), 186–220, arXiv: 1004.1153 | DOI | MR | Zbl

[8] K. G. Chetyrkin, F. V. Tkachov, Nucl. Phys. B, 192:1 (1981), 159–204 | DOI

[9] O. F. de Alcantara Bonfim, J. E. Kirkham, A. J. McKane, J. Phys A: Math. Gen., 13:7 (1980), L247–L251 | DOI

[10] O. F. de Alcantara Bonfim, J. E. Kirkham, A. J. McKane, J. Phys A: Math. Gen., 14:9 (1981), 2391–2413 | DOI

[11] L. Ts. Adzhemyan, M. V. Kompaniets, TMF, 169:1 (2011), 100–111 | DOI | DOI | Zbl

[12] F. Zhong, Q. Chen, Phys. Rev. Lett., 95:17 (2005), 175701, 4 pp. | DOI

[13] M. Fisher, Phys. Rev. Lett., 40:25 (1978), 1610–1613 | DOI

[14] M. Breuer, H.-K. Janssen, Z. Phys. B: Cond. Mat., 41:1 (1981), 55–64 | DOI | MR

[15] C. M. Bender, D. C. Brody, H. F. Jones, Phys. Rev. Lett., 93:25 (2004), 251601, 4 pp., arXiv: hep-th/0402011 | DOI | MR