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math-phJul 1, 2022
2
citations (OpenAlex)
authors
  • Anthony J Guttmann
  • Iwan Jensen
institutions
  • Flinders University
  • The University of Melbourne
arXiv abstractPDF
paper

On the existence of critical exponents for self-avoiding walks

arXiv:2207.08433 · doi:10.1088/1751-8121/ac943a

Abstract

We describe some ideas of John Hammersley for proving the existence of critical exponents for two-dimensional self-avoiding walks and provide numerical evidence for their correctness.

arXiv comment19 pages, 5 figures

References in corpus (8)

  • Accurate estimate of the critical exponent ν for self-avoiding walks via a fast implementation of the pivot algorithm
  • Logarithmic correction for the susceptibility of the 4-dimensional weakly self-avoiding walk: a renormalisation group analysis
  • Self-avoiding walk is sub-ballistic
  • Scale-free Monte Carlo method for calculating the critical exponent γ of self-avoiding walks
  • On the growth constant for square-lattice self-avoiding walks
  • Finite-order correlation length for 4-dimensional weakly self-avoiding walk and ∣φ∣4 spins
  • Square lattice self-avoiding walks and biased differential approximants
  • New scaling laws for self-avoiding walks: bridges and worms

Cited by in corpus (1)

  • Efficient network exploration by means of resetting self-avoiding random walkers
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