We develop a multi order parameter mean-field formalism for systems of coupled quantum rotors. The scheme is developed to account for systems where { \it ortho-para} distinction is valid. We apply our formalism to solid H$_2$ and D$_2$. We find an anomalous { \it reentrant} orientational phase transition for both systems at thermal equilibrium. The correlation functions of the order parameter indicate short-range order at low temperatures. As temperature is increased the correlation increases along the phase boundary. We also find that even extremely small { \it odd-J} concentrations (1%) can trigger short-range orientational ordering.
Categories: cond-mat.stat-mech cond-mat.mtrl-sci