Punctured polygons and polyominoes on the square lattice
نویسندگان
چکیده
منابع مشابه
Punctured polygons and polyominoes on the square lattice
We use the finite lattice method to count the number of punctured staircase and selfavoiding polygons with up to three holes on the square lattice. New or radically extended series have been derived for both the perimeter and area generating functions. We show that the critical point is unchanged by a finite number of punctures, and that the critical exponent increases by a fixed amount for eac...
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We study a proper subset of polyominoes, called polygonal polyominoes, which are defined to be self-avoiding polygons containing any number of holes, each of which is a self-avoiding polygon. The staircase polygon subset, with staircase holes, is also discussed. The internal holes have no common vertices with each other, nor any common vertices with the surrounding polygon. There are no ‘holes-...
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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 ...
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We have developed an improved algorithm that allows us to enumerate the number of self-avoiding polygons on the square lattice to perimeter length 90. Analysis of the resulting series yields very accurate estimates of the connective constant μ = 2.638 158 529 27(1) (biased) and the critical exponent α = 0.500 0005(10) (unbiased). The critical point is indistinguishable from a root of the polyno...
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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 = 4.062570(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 τ >...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2000
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/33/9/303