Enumeration of self-avoiding walks on the square lattice
نویسندگان
چکیده
منابع مشابه
Enumeration of self-avoiding walks on the square lattice
We describe a new algorithm for the enumeration of self-avoiding walks on the square lattice. Using up to 128 processors on a HP Alpha server cluster we have enumerated the number of self-avoiding walks on the square lattice to length 71. Series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and mean-square distance of monomers from the end points h...
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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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According to renormalization group theory, the scaling properties of critical systems are insensitive to microscopic details and are governed by a small set of universal exponents. Polymers can be considered as critical systems in the limit where their length N (the number of chained monomers) grows [1]. For instance, the free energy FN of an isolated polymer in a swollen phase behaves asymptot...
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In the past decade, a lot of attention has been devoted to the enumeration of walks with prescribed steps confined to a convex cone. In two dimensions, this means counting walks in the first quadrant of the plane (possibly after a linear transformation). But what about walks in non-convex cones? We investigate the two most natural cases: first, square lattice walks avoiding the negative quadran...
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We have developed a transfer matrix algorithm for the enumeration of compact self-avoiding walks on rectangular strips of the square lattice. The algorithm is easily adapted to other shapes or generalized to problems such as interacting walks. These models are relevant in the study of globular proteins. 2001 Elsevier Science B.V. All rights reserved. PACS: 05.50.+q; 02.70.Rw; 61.25.Hq
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2004
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/37/21/002