Asymptotically faster algorithm for counting self-avoiding walks and self-avoiding polygons
نویسندگان
چکیده
منابع مشابه
Counting Self-avoiding Walks
The connective constant μ(G) of a graph G is the asymptotic growth rate of the number of self-avoiding walks on G from a given starting vertex. We survey three aspects of the dependence of the connective constant on the underlying graph G. Firstly, when G is cubic, we study the effect on μ(G) of the Fisher transformation (that is, the replacement of vertices by triangles). Secondly, we discuss ...
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We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is applied to the vertex or vertices of the walk located at the maximum distance above the boundary of the half-space. In the case of bridges, this is the unique end-point. In the case of SAWs or self-avoiding polygons, this corresponds to all ver...
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We present a new method for counting self-avoiding walks (SAW’s), called stochastic enumeration (SE), a stochastic replica of the naive (computationally intractable) full enumeration method. Also presented is a new approach, called OSLA-SPLIT, a combination of classic splitting with importance sampling. The latter is based on the well-known method, onestep-look-ahead (OSLA) method. Polynomial c...
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We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monome...
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We enumerate self-avoiding walks and polygons, counted by perimeter, on the quasiperiodic rhombic Penrose and Ammann-Beenker tilings, thereby considerably extending previous results. In contrast to similar problems on regular lattices, these numbers depend on the chosen initial vertex. We compare different ways of counting and demonstrate that suitable averaging improves convergence to the asym...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2019
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8121/ab52b0