Long chains of the $\mathrm{HP}$ lattice protein model are studied by the multi-self-overlap ensemble Monte Carlo method, which was developed recently by Iba, Chikenji, and Kikuchi. This method successfully finds the lowest energy states reported before for sequences of the chain length $N=42\mathrm{}–100$ in two and three dimensions. Moreover, the method realizes the lowest energy state that was ever found in a case of $N=100\mathrm{}$. Finite-temperature properties of these sequences are also investigated by this method. Two successive transitions are observed between the native and random coil states. Thermodynamic analysis suggests that the ground state degeneracy is relevant to the order of the transitions.

• Received 23 February 1999

DOI:https://doi.org/10.1103/PhysRevLett.83.1886