2014/09/30 by Nickolay Izmailian, Ralph Kenna · 1 citation
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.91.022129
published as Phys. Rev. E 91, 022129 (2015) · 13 pages. Expanded text with additional results
arxiv created 2014/10/14 · arxiv updated 2016/10/26
We express the partition functions of the spanning tree on finite square lattices under five different sets of boundary conditions (free, cylindrical, toroidal, Möbius 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. We also explain an apparent discrepancy between logarithmic correction terms in the free energy for a two dimensional spanning tree model with periodic and free boundary conditions and conformal field theory predictions. We have obtain corner free energy for the spanning tree under free boundary conditions in full agreement with conformal field theory predictions.