Resummation of the1nexpansion through a self-consistent approach

Abstract

Bray's self-consistent screening approximation for calculating critical exponents is extended to higher orders, resulting in a scheme equivalent to a resummation of the $\frac{1}{n}$ expansion. While the integration techniques borrowed from conformal invariant field theory reduce the task of evaluating Feynman integrals appearing in this scheme to about the level of a straight $\frac{1}{n}$ calculation, the second-order results obtained here for critical exponents as functions of the order-parameter dimensionality $n$ and space dimensionality $d$ are definitely superior to those of a direct $\frac{1}{n}$ calculation and produce acceptable estimates down to about $n\ensuremath{\simeq}1\ensuremath{-}2$ for $d=3$.