  We use the effective potential method of quantum field theory to obtain the
quantum corrections to the zero temperature phase diagram of systems with
competing order parameters. We are particularly interested in two different
scenarios: regions of the phase diagram where there is a bicritical point, at
which both phases vanish continuously, and the case where both phases coexist
homogeneously. We consider different types of couplings between the order
parameters, including a bilinear one. This kind of coupling breaks
time-reversal symmetry and it is only allowed if both order parameters
transform according to the same irreducible representation. This occurs in many
physical systems of actual interest like competing spin density waves,
different types of orbital antiferromagnetism, elastic instabilities of crystal
lattices, vortices in a multigap SC and also applies to describe the unusual
magnetism of the heavy fermion compound URu2Si2. Our results show that quantum
corrections have an important effect on the phase diagram of systems with
competing orders.
