Generating a non-perturbative mass gap using Feynman diagrams in an asymptotically free theory

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.