The length of self-avoiding walks on the complete graph

Youjin Deng, Timothy M. Garoni, Jens Grimm, Abrahim Nasrawi, Zongzheng Zhou

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We study the variable-length ensemble of self-avoiding walks on the complete graph. We obtain the leading order asymptotics of the mean and variance of the walk length, as the number of vertices goes to infinity. Central limit theorems for the walk length are also established, in various regimes of fugacity. Particular attention is given to sequences of fugacities that converge to the critical point, and the effect of the rate of convergence of these fugacity sequences on the limiting walk length is studied in detail. Physically, this corresponds to studying the asymptotic walk length on a general class of pseudocritical points.

Original languageEnglish
Article number103206
Pages (from-to)1-15
Number of pages15
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number10
Publication statusPublished - 22 Oct 2019


  • classical phase transitions
  • finite-size scaling
  • polymers

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