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

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

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

Statistical Mechanics 2016-02-09 v1

Authors: L. Ts. Adzhemyan , Yu. V. Kirienko , M. V. Kompaniets

Abstract

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 $8\%$ .

Keywords

critical exponent renormalization group phi^4 model o(n) symmetry loop expansion perturbation series borel transformation

Cite

@article{arxiv.1602.02324,
  title  = {Critical exponent $\eta$ in 2D $O(N)$-symmetric $\varphi^4$-model up to 6~loops},
  author = {L. Ts. Adzhemyan and Yu. V. Kirienko and M. V. Kompaniets},
  journal= {arXiv preprint arXiv:1602.02324},
  year   = {2016}
}

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

Abstract

Keywords

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