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

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.

16 pages, 9 figures, jpconf style files. Presented at the conference "Counting Complexity: An international workshop on statistical mechanics and combinatorics." In celebration of Prof. Tony Guttmann's 60th birthday

References in corpus (6)

• Enumeration of self-avoiding walks on the square lattice
• A parallel algorithm for the enumeration of self-avoiding polygons on the square lattice
• Correction-to-scaling exponents for two-dimensional self-avoiding walks
• Self-avoiding walks and polygons on the triangular lattice
• Scaling function and universal amplitude combinations for self-avoiding polygons
• Scaling function for self-avoiding polygons

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• Two-dimensional interacting self-avoiding walks: new estimates for critical temperatures and exponents
• Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices
• On complex singularities of the 2D Euler equation at short times
• A parallel algorithm for the enumeration of benzenoid hydrocarbons
• Area distribution and scaling function for punctured polygons