Scaling behaviour of two-dimensional polygon models

Details Scaling behaviour of two-dimensional polygon models Scaling behaviour of two-dimensional polygon models

2002-02-20

arxiv.org/abs/cond-mat/0202339v2

J. Stat. Phys 108 (2002) 459-493

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1023/A:1015773723188

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.

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