Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-09-10
J. Phys. A: Math. Gen. 34 (2001) 4783-4796
Physics
Condensed Matter
Statistical Mechanics
17 pages, 3 figures
Scientific paper
10.1088/0305-4470/34/23/301
The perimeter and area generating functions of exactly solvable polygon models satisfy q-functional equations, where q is the area variable. The behaviour in the vicinity of the point where the perimeter generating function diverges can often be described by a scaling function. We develop the method of q-linear approximants in order to extract the approximate scaling behaviour of polygon models when an exact solution is not known. We test the validity of our method by approximating exactly solvable q-linear polygon models. This leads to scaling functions for a number of q-linear polygon models, notably generalized rectangles, Ferrers diagrams, and stacks.
Guttmann Anthony J.
Richard Christoph
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