  We study the thermodynamic behavior of a simple off-lattice model for protein
folding. The model is two-dimensional and has two different ``amino acids''.
Using numerical simulations of all chains containing eight or ten monomers, we
examine the sequence dependence at a fixed temperature. It is shown that only a
few of the chains exist in unique folded state at this temperature, and the
energy level spectra of chains with different types of behavior are compared.
Furthermore, we use this model as a testbed for two improved Monte Carlo
algorithms. Both algorithms are based on letting some parameter of the model
become a dynamical variable; one of the algorithms uses a fluctuating
temperature and the other a fluctuating monomer sequence. We find that by these
algorithms one gains large factors in efficiency in comparison with
conventional methods.
