Spin-one-Ising model for (CO)1?x (N2) x mixtures: A finite size scaling study of random-field-type critical phenomena

Abstract

A qualitative model for solid mixtures of diatomic molecules, where one species (called CO, to be specific) carries both a dipole moment and a quadrupole moment, while the other species (calledN 2) has only a quadrupole moment, is studied by Monte Carlo methods. We use spinsS i =±1 to represent the orientations of the CO electric dipole moment, if the lattice sitei is taken by a CO molecule, whileS i =0 if the site is taken by anN 2 molecule. Assuming nearest-neighbor antiferroelectric interactions between CO molecules, and a bilinear dipole-quadrupole coupling between CO andN 2, the randomly quenchedN 2 molecules act like random fields do in the random field Ising model. In previous work it was already shown that this crude model is in very good agreement with experimental data in two dimensions (adsorbed layers), where the random fields induces a rounding of the transition. Here Monte Carlo simulations of the three-dimensional version of this model are presented and analyzed with finite size scaling concepts. As expected from the theory, a behaviour qualitatively different from the two-dimensional case is detected. The Monte Carlo data provide qualitative evidence that the random field induces crossover to an universality class with critical exponents distinct from the pure Ising model, but it is not feasible to us to study large enough systems that would allow a reliable estimation of these exponents. But the results show that dilution without dipole-quadrupole coupling has much less drastic effects on the critical behavior, and that in the presence of this coupling very small impurity concentrations do indeed change the critical behavior.