  Using the example of a two dimensional four-fermion lattice field theory we
demonstrate that Feynman diagrams can generate a mass gap when massless
fermions interact via a marginally relevant coupling. We introduce an infrared
cutoff through the finite system size so that the perturbation series for the
partition function and observables become convergent. We then use the Monte
Carlo approach to sample sufficiently high orders of diagrams to expose the
presence of a mass gap in the lattice model.
