Reentrant Phase Diagram in Ortho-Para Mixtures of Solid H$_{2}$ at High Pressure

Quantum effects dominate the low temperature phase diagram of solid molecular hydrogen in a wide range of pressures from ambient up to about 100 GPa. Important differences exist in the behavior of pure even-$J $(para-H$_{2}$ and ortho-D$_{2})$, and odd-$J$ (ortho-H$_{2}$ and para-D$_{2})$ species, but little is known about the phase diagram of ortho-para mixtures. We develop a multiorder parameter mean-field formalism for systems of coupled quantum rotors and apply it to solid H$_{2}$ and D$_{2}$. For a thermal distribution of ortho-para molecules we find an anomalous reentrant orientational phase transition in the pressure - temperature phase diagram of both systems [Hetenyi et al., PRL 94, 125503 (2005)]. The correlation functions of the order parameter indicate short-range order at low temperatures. As the temperature is increased the correlation increases along the phase boundary. We also find that even extremely small \textit{odd}-$J $concentrations (1{\%}) can trigger short-range orientational ordering.