  We report a numerical study of self-avoiding polymers on the square lattice,
including an attractive potential between nonconsecutive monomers. Using
Wang-Landau sampling (WLS) with adaptive windows, we obtain the density of
states for chains of up to N=300 monomers and associated thermodynamic
quantities. The method enables one to simulate accurately the low-temperature
regime, which is virtually inaccessible using traditional methods. Instead of
defining fixed energy windows, as in usual WLS, this method uses windows with
boundaries that depend on the set of energy values on which the histogram is
flat at a given stage of the simulation. Shifting the windows each time the
modification factor $f$ is reduced, we eliminate border effects that arise in
simulations using fixed windows.
