منابع مشابه
Size and area of square lattice polygons
We use the finite lattice method to calculate the radius of gyration, the first and second area-weighted moments of self-avoiding polygons on the square lattice. The series have been calculated for polygons up to perimeter 82. Analysis of the series yields high accuracy estimates confirming theoretical predictions for the value of the size exponent, ν = 3/4, and certain universal amplitude comb...
متن کاملSelf-avoiding polygons on the square lattice
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...
متن کاملPunctured 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...
متن کاملOsculating and neighbour-avoiding polygons on the square lattice*
We study two simple modifications of self-avoiding polygons (SAPs). Osculating polygons (OP) are a super-set in which we allow the perimeter of the polygon to touch at a vertex. Neighbour-avoiding polygons (NAP) are only allowed to have nearest-neighbour vertices provided these are joined by the associated edge and thus form a sub-set of SAPs. We use the finite lattice method to count the numbe...
متن کاملConvex lattice polygons of fixed area with perimeter-dependent weights.
We study fully convex polygons with a given area, and variable perimeter length on square and hexagonal lattices. We attach a weight tm to a convex polygon of perimeter m and show that the sum of weights of all polygons with a fixed area s varies as s(-theta(conv))eK(t)square root(s) for large s and t less than a critical threshold tc, where K(t) is a t-dependent constant, and theta(conv) is a ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2000
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/33/18/301