2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/198366Within Euclidean lattice field theory an exact equivalence between the one-flavour 2D Thirring model with Wilson fermions and Wilson parameter $r = 1$ to a two-colour loop model on the square lattice is established. For non-interacting fermions this model reduces to an exactly solved loop model which is known to be a free fermion model. The two-colour loop model equivalent to the Thirring model can also be understood as a 4-state 49-vertex model.29 pages LaTeXHigh Energy Physics - LatticeCondensed MatterHigh Energy Physics - Theorytext