Conformal Invariance Predictions for the Three-Dimensional Self-Avoiding Walk

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3 Scopus citations


If the three dimensional self-avoiding walk (SAW) is conformally invariant, then one can compute the hitting densities for the SAW in a half-space and in a sphere (Kennedy in Phys Rev Lett 111: 165703, 2013). The ensembles of SAW’s used to define these hitting densities involve walks of arbitrary lengths, and so these ensembles cannot be directly studied by the pivot Monte Carlo algorithm for the SAW. We show that these mixed length ensembles should have the same scaling limit as certain weighted ensembles that only involve walks with a single length, thus providing a fast method for simulating these ensembles. Preliminary simulations which found good agreement between the predictions and Monte Carlo simulations for the SAW were reported in Kennedy (Phys Rev Lett 111: 165703, 2013). In this paper we present more accurate simulations testing the predictions and find even stronger support for the prediction that the SAW is conformally invariant in three dimensions.

Original languageEnglish (US)
Pages (from-to)1195-1212
Number of pages18
JournalJournal of Statistical Physics
Issue number6
StatePublished - Mar 2015


  • Conformal invariance
  • Self-avoiding walk
  • Three dimensions

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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