Finite temperature phase transition in the 4d compact U(1) 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 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.