Year: 2011
Type: article
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 ≤ d ≤ 10. From the data we compute formulae for perimeter polynomials for lattice animals of size n ≤ 11 in arbitrary dimension d . When amended by combinatorial arguments, the new data suffice to yield explicit formulae for the number of lattice animals of size n ≤ 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.
Authors: Sebastian Luther, Stephan Mertens
Institutions: Otto-von-Guericke-Universität Magdeburg, Santa Fe Institute
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2006207441