Exact Scaling Functions for Self-Avoiding Loops and Branched Polymers

Details Exact Scaling Functions for Self-Avoiding Loops and Branched Polymers Exact Scaling Functions for Self-Avoiding Loops and Branched Polymers

2001-07-11

arxiv.org/abs/cond-mat/0107223v3

J.Phys. A34 (2001) L665-L672

Physics

Condensed Matter

Statistical Mechanics

5 pages; v2: factors of 2 corrected; v.3: relation with existing theta-point results clarified, some references added/updated

Scientific paper

10.1088/0305-4470/34/47/101

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.

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