Scaling function for self-avoiding polygons

Details Scaling function for self-avoiding polygons Scaling function for self-avoiding polygons

2003-02-25

arxiv.org/abs/cond-mat/0302513v1

Iagolnitzer D, Rivasseau V and Zinn-Justin J (eds) Proceedings of the International Congress on Theoretical Physics TH2002 (Pa

Physics

Condensed Matter

Statistical Mechanics

11 pages, 5 figures

Scientific paper

Exactly solvable models of planar polygons, weighted by perimeter and area, have deepened our understanding of the critical behaviour of polygon models in recent years. Based on these results, we derive a conjecture for the exact form of the critical scaling function for planar self-avoiding polygons. The validity of this conjecture was recently tested numerically using exact enumeration data for small values of the perimeter on the square and triangular lattices. We have substantially extended these enumerations and also enumerated polygons on the hexagonal lattice. We also performed Monte-Carlo simulations of the model on the square lattice. Our analysis supports the conjecture that the scaling function is given by the logarithm of an Airy function.

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