Random-field-induced rounding of the Ising-type transition in physisorbed (CO)1-x(N2)x mixtures: Monte Carlo studies of a simple model

Abstract

The authors propose a simple model for (CO)1-x(N2)x mixtures adsorbed on graphite where a lattice site carries a spin Si=+or-1 representing the orientations of the CO electric dipole moment if the site is occupied by a CO molecule, while the spin Si=0 if the site is taken by an N2 molecule, which has a quadrupole moment only. Assuming a bilinear dipole-quadrupole coupling, randomly quenched N2 impurities then act as random fields would act on an Ising antiferromagnet. For simplicity, a square lattice is treated and the range of all interactions is restricted to nearest neighbours. Monte Carlo studies are performed for a range of lattice linear dimensions L from L=24 to L=50, and the specific heat order parameter and susceptibility, as well as the fourth-order cumulant, are studied, applying finite-size scaling concepts where appropriate. The specific heat results display a striking qualitative similarity to the experimental data of Wiechert and Arlt, and provide evidence that the transition is already rounded by arbitrarily small dilution, consistent with theoretical predictions for the two-dimensional random field Ising model. While the experiments needed to rely on the specific heat only, the data for the (strongly rounded) ordering susceptibility and the cumulant (where the common intersection point disappears, consistent with the absence of a transition) provide compelling evidence for this picture. The crossover scaling analysis first proposed by Ferreira et al. for dilute antiferromagnets in a field also works out reasonably well for the present model.