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We present a simple non-equilibrium model of mass condensation withLennard-Jones interactions between particles and the substrate. We show thatwhen some number of particles is deposited onto the surface and the system isleft to equilibrate, particles condense into an island if the density ofparticles becomes higher than some critical density. We illustrate this withnumerically obtained phase diagrams for three-dimensional systems. We alsosolve a two-dimensional counterpart of this model analytically and show thatnot only the phase diagram but also the shape of the cross-sections ofthree-dimensional condensates qualitatively matches the two-dimensionalpredictions. Lastly, we show that when particles are being deposited with aconstant rate, the system has two phases: a single condensate for lowdeposition rates, and multiple condensates for fast deposition. The behaviourof our model is thus similar to that of thin film growth processes, and inparticular to Stranski-Krastanov growth.

A simple non-equilibrium, statistical-physics toy model of thin-film growth