Journal of Statistical Physics, Vol. 58, Nos. 3/4, 1990. p. 475-484.
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 x_c = 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 n^1.5.