Entropy of chains placed on the square lattice

Details Entropy of chains placed on the square lattice Entropy of chains placed on the square lattice

2002-10-02

arxiv.org/abs/cond-mat/0210065v2

Physical Review E, 67, 31803 (2003)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 7 figures

Scientific paper

10.1103/PhysRevE.67.031803

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-and mutually avoiding, and a fraction rho of the sites are occupied by monomers. We solve the problem exactly on stripes of increasing width m and then extrapolate our results to the two-dimensional limit to infinity using finite-size scaling. The extrapolated results for several finite values of M and in the polymer limit M to 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 to infinity, rather precise estimates of the entropy are obtained.

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