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

TL;DR

This paper analyzes the asymptotic behavior of the partition function for self-avoiding polygons on a square lattice, weighted by area, as the area weight approaches one from above, revealing dominant terms and corrections.

Contribution

It provides the first detailed asymptotic analysis of the finite-perimeter partition function for lattice vesicles weighted by area in the inflated regime.

Findings

Derived the dominant asymptotic form of the partition function.

Determined the order of correction terms in the asymptotics.

Examined the approach of q to 1^+ in detail.

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.