RESUMO
Using the transfer matrix technique, we estimate the entropy for a gas of rods of sizes equal to k (named k-mers), which cover completely a square lattice. Our calculations were made considering three different constructions, using periodical and helical boundary conditions. One of those constructions, which we call profile method, was based on the calculations performed by Dhar and Rajesh to obtain a lower limit to the entropy of very large chains placed on the square lattice. This method, so far as we know, was never used before to define the transfer matrix, but turned out to be very useful, since it produces matrices with smaller dimensions than those obtained using the usual approach. Our results were obtained for chain sizes ranging from k=2 to k=10 and they are compared with results already available in the literature. In the case of dimers (k=2) our results are compatible with the exact result. For trimers (k=3), recently investigated by Ghosh et al., also our results were compatible, with the same happening for the simulational estimates obtained by Pasinetti et al. in the whole range of rod sizes. Our results are also consistent with the asymptotic expression for the behavior of the entropy as a function of the size k, proposed by Dhar and Rajesh for very large rods (kâ«1).
RESUMO
By using the transfer matrix approach, we investigate the asymptotic behavior of the entropy of flexible chains with M monomers each placed on strips with periodic boundary conditions (cylinders). In the limit of high density of monomers, we study the behavior of the entropy as a function of the density of monomers and the width of the strip, inspired by recent analytical studies of this problem for the particular case of dimers (M=2). We obtain the entropy in the asymptotic regime of high densities for chains with M=2,...,9 monomers, as well as for the special case of polymers, where M-->infinity, and find that the results show a regular behavior similar to the one found analytically for dimers. We also verify that in the low-density limit the mean-field expression for the entropy is followed by the results from our transfer matrix calculations.
RESUMO
Using the transfer matrix technique, finite-size scaling, phenomenological renormalization group, and conformal invariance ideas, the thermodynamic behavior of a polymer with interacting bonds on a square lattice has been studied. In this model, one monomer that belongs to the polymer has an activity x=e(beta(mu)), while the interactions between bonds of the polymer that are located on opposite edges of elementary squares of the lattice have a statistical weight y=e(-beta(epsilon)), where epsilon is the interaction energy. Next, the phase diagram of the model in the (x,y) plane was found, which shows three phases, two of them being polymerized. Furthermore, the densities of occupied sites and of bond interactions in each phase were calculated, in order to determine the nature of the transitions between the phases. The results obtained are consistent with a second-order transition line between the nonpolymerized and the regular polymerized phase and a first-order transition between the nonpolymerized and the dense polymerized phase. The boundary between both polymerized phases may be of first or second order, and thus evidence for a tricritical point is found.