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Abstract We have developed a theoretical formalism to calculate the orientational phase diagram of ortho–para (or odd-J/even-J) mixtures of homonuclear diatomic molecules in the low-pressure solid phases. In particular, our formalism allows for the explicit disorder present in such mixtrues. While the formalism is general, here we apply it to the quantum anisotropic planar rotor model, a two-dimensional model of coupled rotors. Our calculated phase diagram, separating phases of disorder and short-range order is reentrant, when an equilibrium mixture of odd-J/even-J species is considered. A reentrant phase diagram separating states of disorder and long-range order is known to exist in all-J species in both two and three dimensions. The phase diagram we find for the thermal mixture of odd-J/even-J species exhibits reentrance over a wider range of coupling constants than the corresponding all-J species. We also investigate systems where the odd-J fraction is fixed as a function of temperature. We find that even 1% odd-J mixture exhibits a phase diagram different from the pure even-J case, indicating that the even-J molecules play important role in orientational ordering. [ABSTRACT FROM AUTHOR]