Four-dimensional boson field theory. III. Nontriviality

The results of numerical investigations based on series analysis indicate clearly that the method of phantom fields constructs nontrivial, self-interacting scalar Euclidean boson field theories. It is found that these continuum theories arise as the scaling limit to normal critical points of lattice statistical mechanical models. The character of these theories is numerically indistinguishable from that of a classical theory on the lambda line near the tricritical point