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

Abstract

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/{radical}(2). The present investigation confirms recent findings that the strong coupling lattice Schwinger model becomes critical for {kappa}{sub cr}{approx_equal}0.38{minus}0.39. The phase transition is of second order and lies in the Ising model universality class. Finally, the central charge of the model at criticality is discussed and predicted to be c=1/2. {copyright} {ital 1997} {ital The American Physical Society}