Knot probability for self-avoiding loops on a cubic lattice

Key Findings & Data:A set of N-step loops is generated by attempting to combine pairs of N/2-step self-avoiding walks constructed by a dimerization method.

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Conclusion & Impact:Our method produces knot probabilities slightly higher than those obtained by Yao et al.[1] using a Monte Carlo method to generate loops.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Domain Parameters

Abstract

We investigate the probability for appearance of knots in self-avoiding loops (SALs) on a cubic lattice. A set of N-step loops is generated by attempting to combine pairs of N/2-step self-avoiding walks constructed by a dimerization method. We demonstrate that our method produces unbiased samples of SALs, and study the knot formation probability as a function of loop size. Our method produces knot probabilities slightly higher than those obtained by Yao et al.[1] using a Monte Carlo method to generate loops.

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Cite This Article

KANTOR, Y., KARDAR, M. (2022). Knot probability for self-avoiding loops on a cubic lattice. ARI The Bulletin of the Istanbul Technical University, Cilt: 54 - Sayı: 2, 1–5. https://ajindex.com/articles/448152

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