We present a simple but rigorous mathematical proof, based on well-knowntheorems about power series in the theory of analytic functions, thatthe perturbative series of a large number of scalar field models inlattice quantum field theory, with interaction terms that are given by^2p for p 2, are divergent at all points excepttheir points of reference =0. This is true not only in thecontinuum limit, but on every individual finite lattice as well, for allspacetime dimensions d 3.
Jorge L. deLyra (2026) studied this question.