Aizenmann, Michael2007-08-162007-08-161983https://hdl.handle.net/11299/4557We discuss the Euclidean 44 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 = 44 S2 (0, x). Furthermore, if any such corrections are present in a continuum limit which is used to construct a 44 field theory the limiting theory would be non-interacting. Our analysis extends to ferromagnetic systems of variables which belong to the Simon-Griffiths class.