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Honeycomb lattice polygons and walks as a test of series analysis techniques

Iwan Jensen 2006 J. Phys.: Conf. Ser. 42 163-178   doi: 10.1088/1742-6596/42/1/016  Help

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Iwan Jensen
ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia
E-mail: I.Jensen@ms.unimelb.edu.au

Abstract. We have calculated long series expansions for self-avoiding walks and polygons on the honeycomb lattice, including series for metric properties such as mean-squared radius of gyration as well as series for moments of the area-distribution for polygons. Analysis of the series yields accurate estimates for the connective constant, critical exponents and amplitudes of honeycomb self-avoiding walks and polygons. The results from the numerical analysis agree to a high degree of accuracy with theoretical predictions for these quantities.

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