Results for the strong coupling lattice Schwinger model with Wilson fermions from a study of the equivalent loop model

Salmhofer has demonstrated the equivalence of the strong coupling lattice Schwinger model with Wilson fermions to a self-avoiding loop model on the square lattice with a bending rigidity eta=1/2. The present paper applies two approximate analytical methods to the investigation of critical properties of the self-avoiding loop model for variable eta, discusses their validity, and makes a comparison with known Monte Carlo results. One method is based on the independent loop approximation used in the literature for studying phase transitions in polymers, liquid helium, and cosmic strings. The second method relies on the known exact solution of the self-avoiding loop model with eta=1/root 2. The present investigation confirms recent findings that the strong coupling lattice Schwinger model becomes critical for kappa(cr)similar or equal to 0.38-0.39. The phase transition is of second order and lies in the Ising model universality class. Finally, the central charge of the modal at criticality is discussed and predicted to be c=1/2.