Critical Exponents of the O(N)-symmetric ${\varphi }^4$ Model from the \boldmath{\large{ ${\epsilon }^7$}} Hypergeometric-Meijer Resummation

Abstract

We extract the $\epsilon$-expansion from the recently obtained seven-loop $g$-expansion for the renormalization group functions of the $O(N)$-symmetric model. The different series obtained for the critical exponents $\nu ,\omega$ and $\eta$ have been resummed using our recently introduced hypergeometric-Meijer resummation algorithm. In three dimensions, very precise results have been obtained for all the critical exponents for $N=0,1,2,3$ and $4$. To shed light on the obvious improvement of the predictions at this order, we obtained the divergence of the specific heat critical exponent $\alpha$ for the $XY$ model. We found the result $-0.0123(11)$ which is compatible with the famous experimental result of -0.0127(3) from the specific heat of zero gravity liquid helium superfluid transition while the six-loop Borel with conformal mapping resummation result in literature gives the value -0.007(3). For the challenging case of resummation of the $\epsilon$-expansion series in two dimensions, we showed that our resummation results reflect a significant improvement to the previous six-loop resummation predictions.

arXiv commentIn this version, we used arbitrary parameter which has been optmized and the corresponding errors are estimated

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Cited by in corpus (1)

• Continued functions and perturbation series: Simple tools for convergence of diverging series in $O(n)$-symmetric ${\varphi }^4$ field theory at weak coupling limit