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Stacking models of vesicles and compact clusters. (English) Zbl 1106.82304
Summary: We investigate three simple lattice models of two dimensional vesicles. These models differ in their behavior from the universality class of partially convex polygons, which has been recently established. They do not have the tricritical scaling of those models, and furthermore display a surprising feature: their (perimeter) free energy is discontinuous with an isolated value at zero pressure. We give the full asymptotic descriptions of the generating functions in area and perimeter variables from the q-series solutions and obtain the scaling functions where applicable.
MSC:
82B05Classical equilibrium statistical mechanics (general)
82B20Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
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