Exact finite-size corrections for the spanning-tree model under different boundary conditions

Nickolay Izmailian, Ralph Kenna

Published 2014-09-25Version 1

We express the partition functions of the spanning tree on finite square lattices under five different sets of boundary conditions (free, cylindrical, toroidal, M\"{o}bius strip, and Klein bottle) in terms of a principal partition function with twisted boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the logarithm of the partition function for each case. We have also established several groups of identities relating spanning-tree partition functions for the different boundary conditions.