  Working in the linear sigma model with quarks, we compute the
finite-temperature effective potential in the presence of a weak magnetic
field, including the contribution of the pion ring diagrams and considering the
sigma as a classical field. In the approximation where the pion self-energy is
computed perturbatively, we show that there is a region of the parameter space
where the effect of the ring diagrams is to preclude the phase transition from
happening. Inclusion of the magnetic field has small effects that however
become more important as the system evolves to the lowest temperatures allowed
in the analysis.
