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Counting Lattice Animals in High Dimensions | | Sebastian Luther
; Stephan Mertens
; | | Date: |
6 Jun 2011 | | Abstract: | We present an implementation of Redelemeier’s algorithm for the enumeration
of lattice animals in high dimensional lattices. The implementation is lean and
fast enough to allow us to extend the existing tables of animal counts,
perimeter polynomials and series expansion coefficients in $d$-dimensional
hypercubic lattices for $3 leq dleq 10$. From the data we compute formulas
for perimeter polynomials for lattice animals of size $nleq 11$ in arbitrary
dimension $d$. When amended by combinatorial arguments, the new data suffices
to yield explicit formulas for the number of lattice animals of size $nleq 14$
and arbitrary $d$. We also use the enumeration data to compute numerical
estimates for growth rates and exponents in high dimensions that agree very
well with Monte Carlo simulations and recent predictions from field theory. | | Source: | arXiv, 1106.1078 | | Services: | Forum | Review | PDF | Favorites | |
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