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Interacting Elastic Lattice Polymers: a Study of the Free-Energy of Globular Rings

We introduce and implement a Monte Carlo scheme to study the equilibrium statistics of polymers in the globular phase. It is based on a model of "interacting elastic lattice polymers" and allows a sufficiently good sampling of long and compact configurations, an essential prerequisite to study the scaling behaviour of free energies. By simulating interacting self-avoiding rings at several temperatures in the collapsed phase, we estimate both the bulk and the surface free energy. Moreover from the corresponding estimate of the entropic exponent $α-2$ we provide evidence that, unlike for swollen and $Θ$-point rings, the hyperscaling relation is not satisfied for globular rings.