  A quite unusual diffuse scattering phenomenology was observed in the
single-crystal X-ray diffraction pattern of cubic perovskite BMT
($\mathrm{BaMg}_{1/3}\mathrm{Ta}_{2/3}\mathrm{O}_3$). The intensity of the
scattering is parametrized as a set of cube-like objects located at the centers
of reciprocal space unit cells, resembling very broad and cubic-shaped
(1/2,1/2,1/2)-satellites. BMT belongs to perovskites of formula
AB$'_{1/3}$B$"_{2/3}$O$_{3}$ (A=Mg, B$'=$Ta, B$"=$Mg). The cubes of the
intensity can be attributed to the partial correlations of the occupancies of
the B site. The pair correlation function is the Fourier transform of the
diffuse scattering intensity and the latter's idealized form yields the unusual
property of a power-law correlation decay with distance. Up to now this is
observed only in a few exotic instances of magnetic order or nematic crystals.
Therefore it cannot be classified as a short-range order phenomenon, as in most
situations originating diffuse scattering. A Monte-Carlo search in
configuration space yielded solutions that reproduce faithfully the observed
diffuse scattering. Analysis of the results in terms of the electrostatic
energy and the entropy point to this phase of BMT as a metastable state,
kinetically locked, which could be the equilibrium state just below the melting
point.
