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A comparative study for the pair-creation contact process using series expansions
A comparative study between two distinct perturbative series expansions for
the pair-creation contact process is presented. In contrast to the ordinary
contact process, whose supercritical series expansions provide accurate
estimates for its critical behavior, the supercritical approach does not work
properly when applied to the pair-creation process. To circumvent this problem
a procedure is introduced in which one-site creation is added to the
pair-creation. An alternative method is the generation of subcritical series
expansions which works even for the case of the pure pair-creation process.
Differently from the supercritical case, the subcritical series yields
estimates that are compatible with numerical simulations
Asymptotic behavior of the entropy of chains placed on stripes
By using the transfer matrix approach, we investigate the asymptotic behavior
of the entropy of flexible chains with monomers each placed on stripes. 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 stripe, 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 monomers, as well as for the special case of polymers,
where , 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
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