  We introduce three stochastic cooperative models for particle deposition and
evaporation relevant to ionic self-assembly of nanoparticles with applications
in surface fabrication and nanomedicine. We present a method for mapping a
stochastic model onto the Ising model, which allows us to use the established
results for the Ising model to describe the properties of the system. After
completing the mapping process, we investigate the time dependence of particle
density using the mean field approximation. We complement this theoretical
analysis with Monte Carlo simulations that support our models. These
techniques, which can be used separately or in combination, are useful as
pedagogical tools because they are tractable mathematically and they apply
equally well to many other physical systems with nearest-neighbor interactions
including voter and epidemic models.
