For a two-dimensional lattice $\Lambda$ with $n$ vertices, the number of spanning trees $N_{ ST}(\Lambda)$ grows asymptotically as $\exp(n z_\Lambda)$ in the thermodynamic limit. We present exact integral expression and numerical value for the asymptotic growth constant $z_\Lambda$ for spanning trees on various two-dimensional lattices with more than one type of vertex given in \cite{ Okeeffe}. An exact closed-form expression for the asymptotic growth constant is derived for net 14, and the asymptotic growth constants of net 27 and the triangle lattice have the simple relation $z_{ 27} = (z_{ tri}+\ln 4)/4$. Some integral identities are also obtained.
Categories: cond-mat.stat-mech