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

TL;DR

This paper shows how Feynman diagrams can generate a non-perturbative mass gap in an asymptotically free, two-dimensional four-fermion lattice field theory by combining perturbation theory, infrared cutoff, and Monte Carlo sampling.

Contribution

It introduces a method to demonstrate mass gap generation using Feynman diagrams and Monte Carlo sampling in a lattice field theory with an infrared cutoff.

Findings

Feynman diagrams can produce a mass gap in the model.

Infrared cutoff ensures convergence of the perturbation series.

Monte Carlo sampling reveals the mass gap in the lattice model.

Abstract

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.