2019/08/31 by Bertrand Duplantier, Anthony J Guttmann · 3 citations
Materials Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Critical exponent #Exponent #Material Dynamics and Properties #Relation (database) #Scaling #Scaling law #Theoretical and Computational Physics #Widom scaling #cond-mat.stat-mech #math-ph #math.CO #math.MP
paper · pdf · doi:10.1088/1742-5468/ab4584
published in Journal of Statistical Mechanics Theory and Experiment 2019(10), 104010 (Institute of Physics) · 13 pages, 5 figures. Revised version expands on applicability of these results and adds many references. Dedicated to the memory of Vladimir Rittenberg
openalex created_date 2019/08/22 · arxiv created 2019/09/08 · openalex publication_date 2019/10/01 · arxiv updated 2020/01/29 · openalex updated_date 2026/08/05
Abstract We show how the theory of the critical behaviour of d -dimensional polymer networks gives a scaling relation for self-avoiding bridges that relates the critical exponent for bridges to that of terminally-attached self-avoiding arches, and the correlation length exponent We find In the case of the special transition, we find We provide compelling numerical evidence for this result in both two- and three-dimensions. Another subset of SAWs, called worms , are defined as the subset of SAWs whose origin and end-point have the same x -coordinate. We give a scaling relation for the corresponding critical exponent which is This too is supported by enumerative results in the two-dimensional case.