The Rubber Band Revisited: Wang-Landau Simulation

In this work we apply Wang-Landau simulations to a simple model which has exact solutions both in the microcanonical and canonical formalisms. The simulations were carried out by using an updated version of the Wang-Landau sampling. We consider a homopolymer chain consisting of $N$ monomers units which may assume any configuration on the two-dimensional lattice. By imposing constraints to the moves of the polymers we obtain three different models. Our results show that updating the density of states only after every $N$ monomers moves leads to a better precision. We obtain the specific heat and the end-to-end distance per monomer and test the precision of our simulations comparing the location of the maximum of the specific heat with the exact results for the three types of walks.