Ising model of polarity formation in molecular crystals: from the growth model to the asymptotic equilibrium state

We analyze a layer-by-layer growth model of crystals consisting of dipolar molecules with two directional states. The model is characterized by the assumption of thermal equilibrium formation of new adlayers, whereas previous layers are treated as being "frozen" in the state in which they were formed. Longitudinal and transverse Ising-type nearest neighbor interactions are taken into account. Under such assumptions, bulk polarization is known to arise. We mainly consider asymptotic one- and two-layer statistics after many steps of growth; we have obtained a theorem relating this statistics to thermal equilibrium of an appropriate two-layer system. Local polarization patterns resembling those of ferromagnetism and antiferromagnetism emerge, depending on signs and magnitudes of the coupling constants. We have explored such effects by means of simulations, by a mean field approximation, and by a Bethe-Peierls analysis.