Critical exponent $\eta$ in 2D $O(N)$-symmetric $\varphi^4$-model up to 6~loops

Autor:	Adzhemyan, L. Ts., Kirienko, Yu. V., Kompaniets, M. V.
Rok vydání:	2016
Předmět:	Condensed Matter - Statistical Mechanics
Druh dokumentu:	Working Paper
Popis:	Critical exponent $\eta$ (Fisher exponent) in $O(N)$-symmetric $\varphi^4$-model was calculated using renormalization group approach in the space of fixed dimension $D=2$ up to 6~loops. The calculation of the renormalization constants was performed with the use of $R'$-operation and specific values for diagrams were calculated in Feynman representation using sector decomposition method. Presented approach allows easy automation and generalization for the case of complex symmetries. Also a summation of the perturbation series was obtained by Borel transformation with conformal mapping. The contribution of the 6-th term of the series led to the increase of the Fisher exponent in $O(1)$ model up to $8\%$.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1602.02324 Zobrazit plný text záznamu View this record from Arxiv