STATISTICS OF CONFINED CHAINS .3. HAMILTONIAN PATHS

The entropy of self-avoiding walks embedded in a square lattice has be en Monte Carlo estimated inside plane squares of various side sizes R. The length of the walks ranged from one to R(2) - 1 steps, the maximu m allowed length, which corresponds to the so-called Hamiltonian paths . It was found that if Phi is the ratio of the occupied over the total number of available lattice sites inside the square, the number of co nfigurations Z(Phi) scales to a good approximation as [Y(Phi)]R(2). Th e limiting Y(Phi) curve has then been estimated from the available dat a, and expressed as a fourth-degree polynomial in Phi. A table is give n for Z(1), that is Hamiltonian paths, comparing values obtained from the theoretical relationship given by Orland et al, from the exact enu meration data of Mayer et al, and from the Monte Carlo estimates of th e present work.