[en] The compact U(1) lattice gauge theory for the mixed action is simulated for lattice size 16⁴ near its critical line. Block spin transformations are applied and the resulting flow of the renormalized action is studied in a space of 10 even couplings. Starting on the cold branch at the phase transition a critical fixed point with the leading critical exponent ν≅0.5 is found. On the hot side of the phase transitions a clear flow towards the trivial fixed point is seen and on the cold side above the phase transition a flow towards larger values of β is observed. (orig.)