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,ω and η 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 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 six-loop resummation predictions.