Finite temperature phase transition in the 4d compact lattice gauge theory

We study the phase diagram of the 4d compact U(1) gauge theory as a function of the number of Euclidean time slices. We use the helicity modulus [Nucl. Phys. B 686 (2004) 85] as order parameter to probe the phase transitions. The order of the transition along the phase boundaries is studied and the possibility of a continuum limit is discussed. We present new, strong evidence that the T=0 bulk phase transition is first order.