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

N. Izmailian, Ralph Kenna

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    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.
    Original languageEnglish
    Article number022129
    JournalPhysical Review E
    Volume91
    Issue number2
    DOIs
    Publication statusPublished - 19 Feb 2015

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    Keywords

    • Forecasting
    • Free energy
    • Parallel architectures
    • Asymptotic expansion
    • Conformal field theories
    • Different boundary condition
    • Exact finite-size corrections
    • Free boundary conditions
    • Logarithmic corrections
    • Partition functions
    • Twisted boundary conditions

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