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Tight-binding Hamiltonians with single and multiple orbitals exhibit anintriguing array of magnetic phase transitions. In most cases the spin orderedphases are insulating, while the disordered phases may be either metallic orinsulating. In this paper we report a Determinant Quantum Monte Carlo study ofinteracting electrons in a geometry which can be regarded as a two-dimensionalPeriodic Anderson Model with depleted interacting ($f$) orbitals. For a singledepletion, we observe an enhancement of antiferromagnetic correlations andformation of localized states. For half of the $f$-orbitals regularly depleted,the system exhibits a ferrimagnetic ground state. We obtain a quantitativedetermination of the nature of magnetic order, which we discuss in the contextof Tsunetsugu's theorem, and show that, although the dc conductivity indicatesinsulating behavior at half-filling, the compressibility remains finite.

Compressible Ferrimagnetism in the depleted Periodic Anderson Model