Prudent walks and polygons

Details Prudent walks and polygons Prudent walks and polygons

2008-10-17

arxiv.org/abs/0810.3137v1

Physics

Condensed Matter

Statistical Mechanics

18 pages, 3 figures, IoP style

Scientific paper

We have produced extended series for two-dimensional prudent polygons, based on a transfer matrix algorithm of complexity O$(n^5),$ for a series of length $n.$ We have extended the definition to three dimensions and produced series expansions for both prudent walks and polygons in three dimensions. For prudent polygons in two dimensions we find the growth constant to be smaller than that for the corresponding walks, and by considering three distinct classes of polygons, we find that the growth constant for polygons varies with class, while for walks it does not. We give the critical exponent for both walks and polygons. In the three-dimensional case we estimate the growth constant for both walks and polygons and also estimate the usual critical exponents $\gamma,$ $\nu$ and $\alpha.$

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