Magnetic ordering of random dense packings of freely rotating dipoles

We study random dense packings of Heisenberg dipoles by numerical simulation. The dipoles are at the centers of identical spheres that occupy fixed random positions in space and fill a fraction $\Phi$ of the spatial volume. The parameter $\Phi$ ranges from rather low values, typical of amorphous ensembles, to the maximum $\Phi$=0.64 that occurs in the random-close-packed limit. We assume that the dipoles can freely rotate and have no local anisotropies. As well as the usual thermodynamical variables, the physics of such systems depends on $\Phi$. Concretely, we explore the magnetic ordering of these systems in order to depict the phase diagram in the temperature-$\Phi$ plane. For $\Phi \gtrsim0.49$ we find quasi-long-range ferromagnetic order coexisting with strong long-range spin-glass order. For $\Phi \lesssim0.49$ the ferromagnetic order disappears giving way to a spin-glass phase similar to the ones found for Ising dipolar systems with strong frozen disorder.