Correlations in the two-dimensional random-field Ising model

Using transfer matrices, we calculate the connected and disconnected correlation functions of the random-field Ising model on long strips of width N≤8. The results, where extrapolated to the thermodynamic limit, are in good qualitative agreement with neutron scattering experiments of Birgeneau et al. [Phys. Rev. B 28, 1438 (1983)] on the two-dimensional dilute Ising-like antiferromagnet ${\mathrm{Rb}}_2$ ${\mathrm{Co}}_{0.7}$ ${\mathrm{Mg}}_{0.3}$ ${\mathrm{F}}_4$. For a particular probability distribution of the random field we propose that this model describes an adsorbed monolayer with a doubly degenerate ground state in the presence of frozen impurities and predict some features that could be detected with low-energy electron diffraction experiments on such systems. A modified mean-field theory gives a good qualitative account of the high-temperature behavior of the correlations of this model.