Properties of the quadrupole glass phase in the presence of an external field gradient

The model of solid random ortho-parahydrogen mixtures with infinite-range interactions $J_{ij}$ between ortho-H$_2$ molecules is investigated. The probability distribution of $J_{ij}$ is supposed to be the normal one, with the first moment of the distribution equal to $J_0$. It is shown that introduction of the external electric field gradient $\gamma$ can induce the orientational phase transition with definite critical temperature. The existence of the quadrupolar glass phase is proved in the presence of $\gamma\neq 0$. The effect of ortho-H$_2$ molecules degeneration on the low temperature properties of such systems is demonstrated and the condition of replica-symmetrical solution stability is found. At low temperatures this solution is stable only for large values of $\gamma$ or $J_0$.