Critical exponents of the O(N)-symmetric φ4 model from the ε7 hypergeometric-Meijer resummation

Abstract

We extract the ε-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 ν, ωand η have been resummed using our recently introduced hypergeometricMeijer 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 α 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 ε-expansion series in two dimensions, we showed that our resummation results reflect a significant improvement to the previous sixloop resummation predictions.