We revisit the problem of a two-dimensional polymer ring subject to an
inflating pressure differential. The ring is modeled as a freely jointed closed
chain of N monomers. Using a Flory argument, mean-field calculation and Monte
Carlo simulations, we show that at a critical pressure, pc​∼N−1, the
ring undergoes a second-order phase transition from a crumpled, random-walk
state, where its mean area scales as ∼N, to a smooth state with
∼N2. The transition belongs to the mean-field universality class. At
the critical point a new state of polymer statistics is found, in which
∼N3/2. For p>>pc​ we use a transfer-matrix calculation to derive
exact expressions for the properties of the smooth state.Comment: 9 pages, 8 figure