  In this article we explore the phase diagram associated to the symmetry
breaking of a scalar self interacting theory, induced by temperature and the
presence of an external electric field. For such purpose, first we obtain the
boson propagator, in the presence of a constant external electric field, both
in the weak and strong field strength limits. Novel expansions are derived for
the effective potential, valid for the whole range of temperature. We found
inverse electric catalysis for the weak field region, i.e. a situation where
the critical temperature diminishes as function of the strength of the electric
field whereas for a strong field electric catalysis emerges. These behaviors,
in the weak and strong intensity sectors, are valid for all possible values of
temperature.

High Energy Physics - Phenomenology