Scaling function and universal amplitude combinations for self-avoiding polygons
Abstract
We analyze new data for self-avoiding polygons, on the square and triangular lattices, enumerated by both perimeter and area, providing evidence that the scaling function is the logarithm of an Airy function. The results imply universal amplitude combinations for all area moments and suggest that rooted self-avoiding polygons may satisfy a q-algebraic functional equation.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.