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

L. Ts. Adzhemyan; Yu. V. Kirienko; M. V. Kompaniets

paper

Critical exponent $η$ in 2D $O (N)$ -symmetric $φ^{4}$ -model up to 6~loops

arXiv:1602.02324

Abstract

Critical exponent $η$ (Fisher exponent) in $O (N)$ -symmetric $φ^{4}$ -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 $8%$ .

Critical exponent η in 2D O(N)-symmetric φ4-model up to 6~loops

Abstract

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Critical exponent $η$ in 2D $O (N)$ -symmetric $φ^{4}$ -model up to 6~loops