Self-avoiding walks and polygons on the triangular lattice

Abstract

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 monomer from the end points. For self-avoiding polygons to length 58 we calculate series for the mean-square radius of gyration and the first 10 moments of the area. Analysis of the series yields accurate estimates for the connective constant of triangular self-avoiding walks, $\mu =4.150797226(26)$, and confirms to a high degree of accuracy several theoretical predictions for universal critical exponents and amplitude combinations.

24 pages, 6 figures

References in corpus (9)

• Enumeration of self-avoiding walks on the square lattice
• Self-avoiding polygons on the square lattice
• Universal Properties of Self-Avoiding Walks from Two-Dimensional Field Theory
• A parallel algorithm for the enumeration of self-avoiding polygons on the square lattice
• Algebraic Techniques for Enumerating Self-Avoiding Walks on the Square Lattice
• Universal Amplitude Combinations for Self-Avoiding Walks, Polygons and Trails
• Mean Area of Self-Avoiding Loops
• Scaling function and universal amplitude combinations for self-avoiding polygons
• Size and area of square lattice polygons

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• Analysis of series expansions for non-algebraic singularities
• Logarithmic finite-size scaling of the self-avoiding walk at four dimensions
• Endless self-avoiding walks
• A numerical adaptation of SAW identities from the honeycomb to other 2D lattices
• A solvable non-directed model of polymer adsorption
• On the number of contacts of a floating polymer chain cross-linked with a surface adsorbed chain on fractal structures