  An effective medium model is developed for disordered metamaterials
containing a spatially random distribution of dielectric spheres. Similar to
effective medium models for ordered metamaterials, this model predicts
resonances in the effective permeability and permittivity arising from
electric- and magnetic-dipole Mie resonances in the spheres. In addition, the
model predicts a redshift of the electric resonance with increasing particle
loading. Interestingly, when the particle loading exceeds the percolation
threshold of 33\%, the model predicts that the electric resonance overlaps with
the magnetic resonance, resulting in a negative refractive index.
