TY - JOUR

T1 - Statistics of lattice animals (polyominoes) and polygons

AU - Jensen, Iwan

AU - Guttmann, Anthony J.

PY - 2000/7

Y1 - 2000/7

N2 - 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, τ = 4.062 570(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 τ > 3.903 18. 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 v = 0.641 15(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.

AB - 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, τ = 4.062 570(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 τ > 3.903 18. 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 v = 0.641 15(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.

UR - http://www.scopus.com/inward/record.url?scp=0034725472&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/33/29/102

DO - 10.1088/0305-4470/33/29/102

M3 - Article

AN - SCOPUS:0034725472

VL - 33

SP - L257-L263

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 29

ER -