Scaling function for self-avoiding polygons

Abstract

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.

11 pages, 5 figures

References in corpus (7)

• A parallel algorithm for the enumeration of self-avoiding polygons on the square lattice
• Universal Amplitude Combinations for Self-Avoiding Walks, Polygons and Trails
• Mean Area of Self-Avoiding Loops
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• On the Asymptotics of the Finite-Perimeter Partition Function of Two-Dimensional Lattice Vesicles

Cited by in corpus (5)

• Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces
• Area distribution of the planar random loop boundary
• Honeycomb lattice polygons and walks as a test of series analysis techniques
• Area distribution and scaling function for punctured polygons
• Limit distributions and scaling functions