  It is shown that the infinite dimensional critical surface of general
euclidean lattice actions in a generic four-dimensional scalar field theory
with $\Phi^4$ 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.
