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Using the example of a two dimensional four-fermion lattice field theory wedemonstrate that Feynman diagrams can generate a mass gap when masslessfermions interact via a marginally relevant coupling. We introduce an infraredcutoff through the finite system size so that the perturbation series for thepartition function and observables become convergent. We then use the MonteCarlo approach to sample sufficiently high orders of diagrams to expose thepresence of a mass gap in the lattice model.

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