2008/10/17 by John C. Dethridge, John Dethridge, Timothy M. Garoni +7
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.0810.3137
18 pages, 3 figures, IoP style
arxiv created 2008/10/17 · openalex publication_date 2008/10/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We have produced extended series for two-dimensional prudent polygons, based on a transfer matrix algorithm of complexity O(n5), 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 γ, ν and α.