Continuous chiral transition in strongly coupled compact QED with the standard torus topology

We analyze the phase diagram of compact QED on the torus with a chirally symmetric four fermion interaction. Inside a mean field approximation for the four fermion term, a line of first order phase transitions and another one of second order are found in the $(\beta, G)$ plane. Approaching the second order line a continuum limit can be defined. Critical exponents vary along this line in a similar way as in the non-compact model, suggesting that a non-trivial interacting continuum theory can be constructed.