Symmetry breaking and phase transition in a model of solid hydrogen

An isotropic model of quadrupole interaction with symmetry breaking is used to describe the orientational ordering of molecules in a hydrogen crystal. In the molecular field approximation solutions are obtained with ordering corresponding to different forms of symmetry breaking. The interaction energies in the ground state are compared for these solutions. In an axisymmetric molecular field a phase transition of second kind is established at a temperature of $2.5^\circ\mathrm K$. The dispersion of the long-wave orientational excitations is linear or quadratic depending on the form of the symmetry breaking in the model.