Modified Borel summation of divergent series and critical-exponent estimates for an<i>N</i>-vector cubic model in three dimensions from five-loop ε expansions

Abstract

An approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the exact asymptotic parameters to be known. The method is tested on functions expanded in their asymptotic power series. It is applied to estimating the critical exponent values for an $N$-vector field model, describing magnetic and structural phase transitions in cubic and tetragonal crystals, from five-loop \ensuremath{\epsilon} expansions.