  We review the Extended Mean Field Theory (EMFT) approximation and apply it to
complex, scalar $\phi^4$-theory on the lattice. We study the critical
properties of the Bose condensation driven by a nonzero chemical potential
$\mu$ at both zero and nonzero temperature and determine the $(T,\mu)$ phase
diagram. The results are in very good agreement with recent Monte Carlo data
for all parameter values considered. EMFT can be formulated directly in the
thermodynamic limit which allows us to study lattice spacings for which Monte
Carlo studies are not feasible with present techniques. We find that the EMFT
approximation accurately reproduces many known phenomena of the exact solution,
like the "Silver Blaze" behavior at zero temperature and dimensional reduction
at finite temperature.
