On the Asymptotics of the Finite-Perimeter Partition Function of Two-Dimensional Lattice Vesicles

Abstract

We derive the dominant asymptotic form and the order of the correction terms of the finite-perimeter partition function of self-avoiding polygons on the square lattice, which are weighted according to their area A as q^A, in the inflated regime, q>1. The approach q->1^+ of the asymptotic form is examined.

arXiv commentaccepted for publication in Communications in Mathematical Physics

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• Pressure exerted by a vesicle on a surface
• Asymptotic Behavior of Inflated Lattice Polygons
• Asymptotic behaviour of convex and column-convex lattice polygons with fixed area and varying perimeter
• Area distribution and scaling function for punctured polygons
• Exact solution of pulled, directed vesicles with sticky walls in two dimensions