  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.
