On the growth constant for square-lattice self-avoiding walks

DOI10.1088/1751-8113/49/49/494004zbMath1366.82023arXiv1607.02984OpenAlexW2460420532WikidataQ58082052 ScholiaQ58082052MaRDI QIDQ2960247

Jesper Lykke Jacobsen, Christian R. Scullard, Anthony J. Guttmann

Publication date: 8 February 2017

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.02984

zbMATH Keywords

self-avoiding walksconnective constanttopological transfer matrix

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Statistical mechanics of crystals (82D25) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (7)

Two-dimensional interacting self-avoiding walks: new estimates for critical temperatures and exponents ⋮ Non-invertible symmetries and RG flows in the two-dimensional \(O(n)\) loop model ⋮ The escape transition in a self-avoiding walk model of linear polymers ⋮ Self-avoiding walk on \(\mathbb{Z}^2\) with Yang-Baxter weights: universality of critical fugacity and 2-point function ⋮ Critical scaling of lattice polymers confined to a box without endpoint restriction ⋮ On the existence of critical exponents for self-avoiding walks ⋮ Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices

Cites Work

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• The connective constant of the honeycomb lattice equals \(\sqrt{2+\sqrt 2}\)
• A numerical adaptation of self-avoiding walk identities from the honeycomb to other 2D lattices
• Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley–Lieb algebras
• Critical manifold of the kagome-lattice Potts model
• Transfer matrix computation of critical polynomials for two-dimensional Potts models
• Self-avoiding polygons on the square lattice
• High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials
• A new transfer-matrix algorithm for exact enumerations: self-avoiding polygons on the square lattice
• High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials

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