Geodesic
Epsilon-expansion in the $N$-component $\varphi^4$ model
Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 3, pp. 365-384

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

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. 
@article{TMF_2006_146_3_a1,
     author = {M. D. Missarov and R. G. Stepanov},
     title = {Epsilon-expansion in the $N$-component $\varphi^4$ model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {365--384},
     publisher = {mathdoc},
     volume = {146},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_146_3_a1/}
}
TY  - JOUR
AU  - M. D. Missarov
AU  - R. G. Stepanov
TI  - Epsilon-expansion in the $N$-component $\varphi^4$ model
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2006
SP  - 365
EP  - 384
VL  - 146
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2006_146_3_a1/
LA  - ru
ID  - TMF_2006_146_3_a1
ER  - 
%0 Journal Article
%A M. D. Missarov
%A R. G. Stepanov
%T Epsilon-expansion in the $N$-component $\varphi^4$ model
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2006
%P 365-384
%V 146
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2006_146_3_a1/
%G ru
%F TMF_2006_146_3_a1
M. D. Missarov; R. G. Stepanov. Epsilon-expansion in the $N$-component $\varphi^4$ model. Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 3, pp. 365-384. http://geodesic.mathdoc.fr/item/TMF_2006_146_3_a1/