  We compute the zero-temperature equation of state of a mixture of two
fermionic atomic species with repulsive interspecies interactions using
second-order perturbation theory. We vary the interaction strength, the
population and the mass imbalance, and we analyze the competition between
different states: homogeneous, partially separated and fully separated. The
canonical phase diagrams are determined for various mass ratios, including the
experimentally relevant case of the 6Li-40K mixture. We find substantial
differences with respect to the equal-mass case: phase separation occurs at
weaker interaction strength, and the partially-separated state can be stable
even in the limit of a large majority of heavy atoms. We highlight the effects
due to correlations by making comparison with previous mean-field results.
