On the Renormalized Coupling Constant of ( 4)4 Field Theory

Abstract

We show, apart from a correlation inequality for the 6-point function, that the critical or continuum limit of (φ^4)_4 lattice field theory is trivial, if some deviations from the mean field theory law are present at the critical point, and if we impose a mild behavior of bare 4-point coupling constant as we approach the critical point. These results are derived from the bounds on the renormalized coupling constant of lattice (φ^4)_d field theory.