For a lattice Λ with n vertices and dimension d equal to or higher than 2, the number of spanning trees NST(Λ) increases asymptotically as exp(nzΛ) in the thermodynamic limit. We present exact integral expressions for the asymptotic growth constant z Λ for spanning trees on several lattices. By taking different unit cells in the calculation, many integral identities can be obtained. We also give zΛ(p) on the homeomorphic expansion of k-regular lattices with p vertices inserted on each edge.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)