On the renormalized coupling constant and the susceptibility in φ44 field theory and the Ising model in four dimensions

We discuss the euclidean φ₄⁴ field theory, and the critical behavior in ferromagnetic systems in four dimensions. It is rigorously shown that there are at most logarithmic corrections to the mean field law in the behavior of the magnetic susceptibility _X = ΣS₂(0, x). Furthermore, if any such corrections are present in a continuum limit which is used to construct a φ₄⁴ field theory, the limiting theory would be non-interacting. Our analysis extends to ferromagnetic systems of variables which belong to the Griffiths-Simon class.