First Order Phase Transition of a Long Polymer Chain

Abstract

We consider a model consisting of a self-avoiding polygon occupying a variable density of the sites of a square lattice. A fixed energy is associated with each $90^{\circ }$-bend of the polygon. We use a grand canonical ensemble, introducing parameters $\mu$ and $\beta$ to control average density and average (total) energy of the polygon, and show by Monte Carlo simulation that the model has a first order, nematic phase transition across a curve in the $\beta$-$\mu$ plane.

11 pages, 7 figures

References in corpus (2)

• Statistical distributions in the folding of elastic structures
• Layering in Crumpled Sheets