Entropy of chains placed on the square lattice.
We obtain the entropy of flexible linear chains composed of M monomers placed on the square lattice using a transfer matrix approach. An excluded volume interaction is included by considering the chains to be self-avoiding and mutually avoiding, and a fraction rho of the sites is occupied by monomers. We solve the problem exactly on stripes of increasing width m and then extrapolate our results to the two-dimensional limit m--> infinity using finite-size scaling. The extrapolated results for several finite values of M and in the polymer limit M--> infinity for the cases where all lattice sites are occupied (rho=1) and for the partially filled case rho<1 are compared with earlier results. These results are exact for dimers (M=2) and full occupation (rho=1) and derived from series expansions, mean-field-like approximations, and transfer matrix calculations for some other cases. For small values of M, as well as for the polymer limit M--> infinity, rather precise estimates of the entropy are obtained.
Dantas
Wellington G
WG
Instituto de Física, Universidade Federal Fluminense, Campus da Praia Vermelha, Niterói, Rio de Janeiro 24210-340, Brazil. wgd@if.uff.br
Stilck
Jürgen F
JF