Size and area of square lattice polygons

Abstract

We use the finite lattice method to calculate the radius of gyration, the first and second area-weighted moments of self-avoiding polygons on the square lattice. The series have been calculated for polygons up to perimeter 82. Analysis of the series yields high accuracy estimates confirming theoretical predictions for the value of the size exponent, $ν=3/4$, and certain universal amplitude combinations. Furthermore, a detailed analysis of the asymptotic form of the series coefficients provide the firmest evidence to date for the existence of a correction-to-scaling exponent, $Δ= 3/2$.