Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A model of compact polymers on a family of three-dimensional fractal
  lattices   We study Hamiltonian walks (HWs) on the family of three--dimensional modified
Sierpinski gasket fractals, as a model for compact polymers in nonhomogeneous
media in three dimensions. Each member of this fractal family is labeled with
an integer $b\geq 2$. We apply an exact recursive method which allows for
explicit enumeration of extremely long Hamiltonian walks of different types:
closed and open, with end-points anywhere in the lattice, or with one or both
ends fixed at the corner sites, as well as some Hamiltonian conformations
consisting of two or three strands. Analyzing large sets of data obtained for
$b=2,3$ and 4, we find that numbers $Z_N$ of Hamiltonian walks, on fractal
lattice with $N$ sites, for $N\gg 1$ behave as $Z_N\sim \omega^N
\mu^{N^\sigma}$. The leading term $\omega^N$ is characterized by the value of
the connectivity constant $\omega>1$, which depends on $b$, but not on the type
of HW. In contrast to that, the stretched exponential term $\mu^{N^\sigma}$
depends on the type of HW through constant $\mu<1$, whereas exponent $\sigma$
is determined by $b$ alone. For larger $b$ values, using some general features
of the applied recursive relations, without explicit enumeration of HWs, we
argue that asymptotical behavior of $Z_N$ should be the same, with $\sigma=\ln
3/\ln[b(b+1)(b+2)/6]$, valid for all $b>2$. This differs from the formulae
obtained recently for Hamiltonian walks on other fractal lattices, as well as
from the formula expected for homogeneous lattices. We discuss the possible
origin and implications of such result.

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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an