  Some time ago Salmhofer demonstrated the equivalence of the strong coupling
lattice Schwinger model with Wilson fermions to a certain 8-vertex model which
can be understood as a self-avoiding loop model on the square lattice with
bending rigidity $\eta = 1/2$ and monomer weight $z = (2\kappa)^{-2}$. The
present paper applies two approximate analytical methods to the investigation
of critical properties of the self-avoiding loop model with variable bending
rigidity, discusses their validity and makes comparison with known MC 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 bending rigidity $\eta = 1/\sqrt{2}$. The present
investigation confirms recent findings that the strong coupling lattice
Schwinger model becomes critical for $\kappa_{cr} \simeq 0.38-0.39$. The phase
transition is of second order and lies in the Ising model universality class.
Finally, the central charge of the strong coupling Schwinger model at
criticality is discussed and predicted to be $c = 1/2$.

High Energy Physics - Lattice;Condensed Matter;High Energy Physics - Theory