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Some time ago Salmhofer demonstrated the equivalence of the strong couplinglattice Schwinger model with Wilson fermions to a certain 8-vertex model whichcan be understood as a self-avoiding loop model on the square lattice withbending rigidity $\eta = 1/2$ and monomer weight $z = (2\kappa)^{-2}$. Thepresent paper applies two approximate analytical methods to the investigationof critical properties of the self-avoiding loop model with variable bendingrigidity, discusses their validity and makes comparison with known MC results.One method is based on the independent loop approximation used in theliterature for studying phase transitions in polymers, liquid helium and cosmicstrings. The second method relies on the known exact solution of theself-avoiding loop model with bending rigidity $\eta = 1/\sqrt{2}$. The presentinvestigation confirms recent findings that the strong coupling latticeSchwinger model becomes critical for $\kappa_{cr} \simeq 0.38-0.39$. The phasetransition is of second order and lies in the Ising model universality class.Finally, the central charge of the strong coupling Schwinger model atcriticality is discussed and predicted to be $c = 1/2$.Comment: 22 pages LaTeX, 6 Postscript figure

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