Exponential Growth Constants for Spanning Forests on Archimedean Lattices: Values and Comparisons of Upper Bounds

We compare our upper bounds on the exponential growth constant $\varphi (\mathrm{\Lambda })$ characterizing the asymptotic behavior of spanning forests on Archimedean lattices $\mathrm{\Lambda }$ with recently derived upper bounds. Our upper bounds on $\varphi (\mathrm{\Lambda })$, which are very close to the respective values of $\varphi (\mathrm{\Lambda })$ that we have calculated, are shown to be significantly better for these lattices than the new upper bounds.