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Symmetry restoration in a theory of a self-interacting charged scalar fieldat finite temperature and in the presence of an external magnetic field isexamined. The effective potential is evaluated nonperturbatively in the contextof the optimized perturbation theory method. It is explicitly shown that in allranges of the magnetic field, from weak to large fields, the phase transitionis second order and that the critical temperature increases with the magneticfield. In addition, we present an efficient way to deal with the sum over theLandau levels, which is of interest especially in the case of working with weakmagnetic fields.

Optimized perturbation theory for charged scalar fields at finite temperature and in an external magnetic field