2001/07/31 by John Cardy · 2 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Mathematical Dynamics and Fractals #cond-mat.stat-mech #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/0305-4470/34/47/101
published as J.Phys. A34 (2001) L665-L672 · 5 pages; v2: factors of 2 corrected; v.3: relation with existing theta-point results clarified, some references added/updated
arxiv created 2001/09/24 · openalex publication_date 2001/11/21 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
It is shown that a recently conjectured form for the critical scaling function for planar self-avoiding polygons weighted by their perimeter and area also follows from an exact renormalization group flow into the branched polymer problem, combined with the dimensional reduction arguments of Parisi and Sourlas. The result is generalized to higher-order multicritical points, yielding exact values for all their critical exponents and exact forms for the associated scaling functions.