Critical indices in three dimensions

Abstract

A modification of Wilson's epsilon -expansion scaling procedure is adapted to direct calculation in three dimensions. The parameter log r is replaced by (r^{- epsilon} 2/-1) where r=t^gamma (t=temperature) and all calculations are carried out directly at epsilon =1. Several conclusions are drawn: (i) Numerical agreement with the best known data for gamma and eta is excellent (1% in gamma and 10% in eta ) whereas the corresponding values are far less good in the epsilon -expansion where eta is off by a factor of more than two. (ii) The series appears to converge very well when corrections to the leading term are summed two by two. (iii) Extrapolations of the early orders of the epsilon -expansion to epsilon =1 are unjustified.