Regular models for solid hydrogen: I

Abstract

Unsymmetric regular models in which molecules on a lattice exist in two states with unequal degeneracies and unequal energies for pairs of like nearest neighbours are investigated. The lattice distribution probabilities are shown to be equal to those of the Ising model under a temperature dependent external field. However, where the energy of formation of a pair of unlike nearest neighbours is positive the model's behaviour is quite different from that of an Ising ferromagnet, since either the configurational specific heat is a continuous function of temperature or there is a first-order transition with latent heat evolved. An unsymmetric regular model is appropriate to solid orthohydrogen when the interactions are of quadrupole—quadrupole type. In general nearest-neighbour pair energies derived from the quadrupole—quadrupole interaction are found to be dependent on the orientation of the line joining the two sites, but for the simple and bodycentred cubic lattices and certain quantization directions this dependence is not apparent. In these cases no transition is found.