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We study symmetry restoration at finite temperature in the theory of a charged scalar field interacting with a constant, external magnetic field. We compute the finite temperature effective potential including the contribution from ring diagrams. We show that in the weak field case, the presence of the field produces a stronger first order phase transition and that the temperature for the onset of the transition is lower, as compared to the case without magnetic field.

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Centaurus A (Cen A) is the nearest radio-loud AGN and is detected from radio to very high energy gamma-rays. Its nuclear spectral energy distribution (SED) shows a double-peak feature, which is well explained by the leptonic synchrotron + synchrotron self-Compton model. This model however cannot account for the observed high energy photons in the TeV range, which display a distinct component. Here we show that ∼ TeV photons can be well interpreted as the π 0 decay products from pγ interactions of Fermi accelerated high energy protons in the jet with the seed photons around the second SED peak at ∼ 170 keV. Extrapolating the inferred proton spectrum to high energies, we find that this same model is consistent with the detection of 2 ultra-highenergy cosmic ray events detected by Pierre Auger Observatory from the direction of Cen A. We also estimate the GeV neutrino flux from the same process, and find that it is too faint to be detected by current high-energy neutrino detectors.