  We present a DFT study utilizing the Hubbard U correction to probe structural
and magnetic disorder in $\mathrm{NaO_{2}}$, primary discharge product of
Na-O$_2$ batteries. We show that $\mathrm{NaO_{2}}$ exhibits a large degree of
rotational and magnetic disorder; a 3-body Ising Model is necessary to capture
the subtle interplay of this disorder. MC simulations demonstrate that
energetically favorable, FM phases near room temperature consist of alternating
bands of orthogonally-oriented $\mathrm{O_{2}}$ dimers. We find that bulk
structures are insulating, with a subset of FM structures showing a moderate
gap ($<2$ eV) in one spin channel.
