Self-avoiding polygons on the square lattice
Abstract
We have developed an improved algorithm that allows us to enumerate the number of self-avoiding polygons on the square lattice to perimeter length 90. Analysis of the resulting series yields very accurate estimates of the connective constant
μ=2.63815852927(1)
(biased) and the critical exponent
α=0.5000005(10)
(unbiased). The critical point is indistinguishable from a root of the polynomial
581
x
4
+7
x
2
−13=0.
An asymptotic expansion for the coefficients is given for all
n.
There is strong evidence for the absence of any non-analytic correction-to-scaling exponent.