A parallel algorithm for the enumeration of self-avoiding polygons on the square lattice

Abstract

We have developed a parallel algorithm that allows us to enumerate the number\nof self-avoiding polygons on the square lattice to perimeter length 110. We\nhave also extended the series for the first 10 area-weighted moments and the\nradius of gyration to 100. Analysis of the resulting series yields very\naccurate estimates of the connective constant $\\mu =2.63815853031(3)$ (biased)\nand the critical exponent $\\alpha = 0.5000001(2)$ (unbiased). In addition we\nobtain very accurate estimates for the leading amplitudes confirming to a high\ndegree of accuracy various predictions for universal amplitude combinations.\n