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      Conformal invariance predictions for the three-dimensional self-avoiding walk

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          Abstract

          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. 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 [14]. 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.

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          Most cited references5

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          Conformal invariance and surface critical behavior

          John Cardy (1984)
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            Self-avoiding walk in five or more dimensions I. The critical behaviour

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              THE LACE EXPANSION FOR SELF-AVOIDING WALK IN FIVE OR MORE DIMENSIONS

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                Author and article information

                Journal
                2014-08-20
                2014-12-22
                Article
                10.1007/s10955-014-1183-8
                1408.4787
                59148eee-d842-4357-aae7-fd76237a5e03

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                82B41
                22 pages, 4 figures. Version 2 corrected typos and changed the exposition in section 3, but no changes to conclusions
                math-ph math.MP math.PR

                Mathematical physics,Mathematical & Computational physics,Probability
                Mathematical physics, Mathematical & Computational physics, Probability

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