https://doi.org/10.1140/epjc/s10052-021-08884-5
Regular Article – Theoretical Physics
Critical exponents of the O(N)-symmetric 
model from the 
hypergeometric-Meijer resummation
Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, 2713, Doha, Qatar
Received:
13
November
2020
Accepted:
14
January
2021
Published online:
27
January
2021
We extract the 
-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 
and 
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 
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 
for the XY model. We found the result 
which is compatible with the famous experimental result of 
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 
. For the challenging case of resummation of the -expansion series in two dimensions, we showed that our resummation results reflect a significant improvement to the previous six-loop resummation predictions.
© The Author(s) 2021
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