Geodesic
Epsilon-expansion in the $N$-component $\varphi^4$ model
Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 3, pp. 365-384 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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