  We investigate the Bose-Einstein condensation patterns, the critical and
multicritical behaviors of three-dimensional mixtures of bosonic gases with
short-range density-density interactions. These systems have a global U(1)+U(1)
symmetry, as the system Hamiltonian is invariant under independent U(1)
transformations acting on each species. In particular, we consider the
three-dimensional Bose-Hubbard model for two lattice bosonic gases coupled by
an on-site inter-species density-density interaction. We study the phase
diagram and the critical behaviors along the transition lines characterized by
the Bose-Einstein condensation of one or both species. We present mean-field
calculations and numerical finite-size scaling analyses of quantum Monte Carlo
data. We also consider multicritical points, close to which it is possible to
observe the condensation of both gas components. We determine the possible
multicritical behaviors by using field-theoretical perturbative methods. We
consider the U(1)+U(1)-symmetric Landau-Ginzburg-Wilson Phi4 theory and
determine the corresponding stable fixed points of the renormalization-group
flow. The analysis predicts that, in all cases, the multicritical behavior is
analogous to the one that would be observed in systems of two identical gases,
with an additional Z_2 exchange symmetry.
