Nontrivial Fixed Point in the 4D $Φ^4$ Lattice Model with Internal $O(N)$ Symmetry

Abstract

It is shown that the infinite dimensional critical surface of general euclidean lattice actions in a generic four-dimensional scalar field theory with $Φ^4$ interactions has a domain of special multicritical points where higher dimensional operators play a special role. Renormalized trajectories of higher derivative continuum field theories with nontrivial interactions are traced back to special ultraviolet stable fixed points on the manifold of multicritical points. These fixed points have an infinite number of relevant directions which identify the universality classes of critical higher derivative field theories. The relevance of the new fixed point structure is discussed within the context of the triviality Higgs mass bound.