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

Understand

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.