Using the example of a two dimensional four-fermion lattice field theory, we show that Feynman diagrams can generate a mass gap in a theory with massless fermions that interact via a marginally relevant coupling. We show this by introducing an infrared cutoff that makes the perturbation series for the partition function convergent. One can then use a Monte Carlo approach to sample sufficiently high orders of diagrams and thus expose the presence of the mass gap. Finally we outline the challenges of applying this method to gauge theories.

Theoretical Developments