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

N. Sh. Izmailian1,2,* and R. Kenna1,†

  • 1Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom
  • 2Yerevan Physics Institute, Alikhanian Brothers 2, 375036 Yerevan, Armenia

  • *ab5223@coventry.ac.uk; izmail@yerphi.am
  • †r.kenna@coventry.ac.uk
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Phys. Rev. E 91, 022129 – Published 19 February, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.022129

Abstract

We express the partition functions of the spanning tree on finite square lattices under five different sets of boundary conditions 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 obtained corner free energy for the spanning tree under free-boundary conditions in full agreement with conformal field theory predictions.

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Phys. Rev. E 91, 022129– Published 19 February, 2015
  • Received 14 October 2014

©2015 American Physical Society

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