Statistics of lattice animals (polyominoes) and polygons

Details Statistics of lattice animals (polyominoes) and polygons Statistics of lattice animals (polyominoes) and polygons

2000-07-14

arxiv.org/abs/cond-mat/0007238v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, 2 eps figures

Scientific paper

10.1088/0305-4470/33/29/102

We have developed an improved algorithm that allows us to enumerate the number of site animals (polyominoes) on the square lattice up to size 46. Analysis of the resulting series yields an improved estimate, $\tau = 4.062570(8)$, for the growth constant of lattice animals and confirms to a very high degree of certainty that the generating function has a logarithmic divergence. We prove the bound $\tau > 3.90318.$ We also calculate the radius of gyration of both lattice animals and polygons enumerated by area. The analysis of the radius of gyration series yields the estimate $\nu = 0.64115(5)$, for both animals and polygons enumerated by area. The mean perimeter of polygons of area $n$ is also calculated. A number of new amplitude estimates are given.

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