Abstract
In the main part of this lecture, we shall discuss the calculation of the critical exponents of the n-vector model in 3 dimensions, using field theoretical techniques [1,2]. This calculation is based on a perturbative expansion at fixed dimension of the various renormalization group (R.G.) functions. Since in 3 dimensions the fixed point S4 coupling constant is not small, the perturbative expansion has to be resummed. We shall present a summation technique using a Borel transformation and a conformal mapping on the variable, argument of the Borel transform. Such a conformal mapping has been made possible by the existence of methods to evaluate the large order behavior of perturbation theory [3].
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