Non-perturbative description of self-interacting charged scalar field at finite temperature and in the presence of an external magnetic field

It is studied the symmetry restoration in a theory of a self-interacting charged scalar field at finite temperature and in the presence of an external magnetic field. The effective potential is evaluated nonperturbatively through the Optimized Perturbation Theory (OPT) nonperturbative method. In addition, we present an efficient numeric way to deal with the sum over the Landau levels in the case of working with weak magnetic fields