double layer formation with embedded clusters with $N=600$). Runs where performed up to three weeks to assure that the lifetime of the metastable configuration is at least an order of magnitude larger than its formation time. Run times for particular cases are given with the resutls in Sec. \[sectionMCfilm\].

In order to simulate larger systems with many clusters we derive in Sec. \[sectionClusterPot\] an effective cluster-cluster potential. Runs are then performed with a few hundred clusters to illustrate the cluster diffusion and fusion process in Sec.\[sectionMCislands\].

Substrate characterization {#sectionsurface}
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The observed formation of the islands as shown in Fig. \[expfig1\] implies that the substrate surface is free of strong pinning centers. The same conclusion can be drawn from oval shapes of the islands with smooth boundaries. Moreover, the pattern formation of the Au film discussed in Sec. \[sectionIsland\] \[Fig.\[expfig1\](c)\] strongly suggest the presence of smooth areas on the substrate surface.

Since this observation is not ad hoc intuitive for an amorphous substrate we investigated the substrate with off-axis holography experiments. In order to obtain a qualitative understanding of the underlying mechanisms of the island formation we determine the substrate-adsorbate interactions via DFT calculations. The latter are used as input 