The exact equivalence of the one-flavour lattice Thirring model with   Wilson fermions to a two-colour loop model
  Within 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. 
K. Scharnhorst (University of Wales Swansea and Humboldt University   Berlin)