Scaling behaviour of two-dimensional polygon models

Abstract

Exactly solvable two-dimensional polygon models, counted by perimeter and area, are described by $q$-algebraic functional equations. We provide techniques to extract the scaling behaviour of these models up to arbitrary order and apply them to some examples. These are then used to analyze the unsolved model of self-avoiding polygons, where we numerically confirm predictions about its scaling function and its first two corrections to scaling.

32 pages, 1 figure; small changes in section 4; journal reference added

References in corpus (3)

• Scaling function and universal amplitude combinations for self-avoiding polygons
• Exact Scaling Functions for Self-Avoiding Loops and Branched Polymers
• q-linear approximants: Scaling functions for polygon models

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