A monte carlo study of ring polymers in disordered systems

We study the properties of ring polymers in disordered systems using a Monte Carlo algorithm. The algorithm is used to generate a ring on a two dimensional lattice, and the disorder is represented by the random dilution of the lattice. We show how the ring undergoes a cross-over from obeying self avoiding statistics at low concentrations of disorder, to behaving like a branched polymer as the concentration of disorder is increased. We find a scaling behavior to characterize this cross-over phenomenon. We further show how this scaling behavior is also present in another class of problems, namely two dimensional vesicles Subject to a pressure differential.