  We demonstrate the feasibility of performing sufficient configurational
sampling of disordered oxides directly from first principles without resorting
to the use of fitted models such as cluster expansion. This is achieved by
harnessing the power of modern-day cluster supercomputers using the replica
exchange Monte Carlo method coupled directly with structural relaxation and
energy calculation performed by density functional codes. The idea is applied
successfully to the calculation of the temperature-dependence of the degree of
inversion in the cation sublattice of MgAl$_2$O$_4$ spinel oxide. The
possibility of bypassing fitting models will lead to investigation of
disordered systems where cluster expansion is known to perform badly: for
example, systems with large lattice deformation due to defects, or systems
where long-range interactions dominate such as electrochemical interfaces.
