Scaling function and universal amplitude combinations for self-avoiding polygons

Details Scaling function and universal amplitude combinations for self-avoiding polygons Scaling function and universal amplitude combinations for self-avoiding polygons

2001-07-16

arxiv.org/abs/cond-mat/0107329v2

J.Phys. A34 (2001) L495-L501

Physics

Condensed Matter

Statistical Mechanics

9 pages

Scientific paper

10.1088/0305-4470/34/36/102

We analyze new data for self-avoiding polygons, on the square and triangular
lattices, enumerated by both perimeter and area, providing evidence that the
scaling function is the logarithm of an Airy function. The results imply
universal amplitude combinations for all area moments and suggest that rooted
self-avoiding polygons may satisfy a $q$-algebraic functional equation.

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