Statistical mechanics of the deformable droplets on flat surfaces

A comprehensive statistical mechanics treatment of (non)interacting deformable planar droplets of arbitrary rigidity is developed. Closed form exact analytic results are obtained for the area statistics of a single droplet and for the decay rates of metastable states characteristic of the first‐order phase transitions for an assembly of such droplets. To select the correct form of the interaction between the droplets, the reparametrization invariance is taken into account. Most of the known two‐dimensional lattice models are obtained as the limiting cases of the interacting droplet model discussed in the text.