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

TL;DR

This paper calculates the critical exponent η in the 2D O(N) φ^4 model up to six loops using advanced renormalization group techniques, providing more precise estimates relevant for phase transition studies.

Contribution

The authors perform a six-loop calculation of η in the 2D O(N) model using a novel automated approach and series summation, improving accuracy over previous lower-order results.

Findings

Six-loop calculation increases η by up to 8% in the O(1) model.

Automated method simplifies complex diagram evaluations.

Series summation enhances the precision of critical exponent estimates.

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 $8\%$.