On the area of square lattice polygons

Abstract

We consider the generating function of self-avoiding square lattice polygons grouped by both area and perimeter. The generating function for polygons of area n is found to diverge at xc=0.251834, with an exponent of zero. The mean perimeter of polygons with area n is found to be proportional to n, while the mean area of polygons with perimeter n is found to be proportional to n1.5. © 1990 Plenum Publishing Corporation.