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

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We study the pure compact U(1) gauge theory with the extended Wilson action (β, γcouplings) 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 support the idea of a weaker, but still first order, phase transition. For negative values of gamma 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 < nu < 0.5, which becomes nu compatible with 1/d when larger lattices are used.