# The s 4 field theory near dimension 4

# The s 4 field theory near dimension 4

This chapter explains how the asymptotic renormalization group equations (RGE), introduced without too much justification in Section 10.6, can be proved within the framework of statistical (or quantum) field theory. The proof is based on the methods of perturbative statistical field theory introduced in Chapter 12, and a few assumptions that it is thus possible to clarify. The discussion is restricted to theories with an Ising type symmetry and the field s has only one component. Generalization to models with *N*-component fields and *O* (*N*) symmetry is simple.

*Keywords:*
renormalization group, RGE, O(N) symmetry, quantum field theory, Ising type symmetry

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