First order signatures in 4D pure compact U(1) gauge theory with toroidal and spherical topologies

We study the pure compact U(1) gauge theory with the extended Wilson action (β, γ couplings) by finite size scaling techniques, in lattices ranging from L=6 to L=24 in the region of γ≤0 with toroidal and spherical topologies. The phase transition presents a double peak structure which survives in the thermodynamical limit in the torus. In the sphere the evidence supports the idea of a weaker, but still first order, phase transition. For γ<0 the transition becomes weaker and larger lattices are needed to find its asymptotic behaviour. Along the transient region the behaviour is the typical one of a weak first order transition for both topologies, with a region where 1/d<ν<0.5, which becomes ν≈1/4 when larger lattices are used.