  We study weakly-repulsive Bose-Bose mixtures in two and three dimensions at
zero temperature using the functional renormalization group (FRG). We examine
the RG flows and the role of density and spin fluctuations. We study the
condition for phase separation and find that this occurs at the mean-field
point within the range of parameters explored. Finally, we examine the energy
per particle and condensation depletion. We obtain that our FRG calculations
compare favorably with known results from perturbative approaches for
macroscopic properties.
