Statistics of close-packed dimers on fractal lattices

We study the model of close-packed dimers on planar lattices belonging to the family of modified rectangular (MR) fractals, whose members are enumerated by an integer $p\geq 2$, as well as on the non-planar 4-simplex fractal lattice. By applying an exact recurrence enumeration method, we determine the asymptotic forms for numbers of dimer coverings, and numerically calculate entropies per dimer in the thermodynamic limit, for a sequence of MR lattices with $2\leq p\leq8$ and for 4-simplex fractal. We find that the entropy per dimer on MR fractals is increasing function of the scaling parameter $p$, and for every considered $p$ it is smaller than the entropy per dimer of the same model on $4$-simplex lattice. Obtained results are discussed and compared with the results obtained previously on some translationally invariant and fractal lattices.
Comment: 15 pages, 9 figures, 2 tables