不同边界条件下生成树模型的精确有限尺寸修正
Exact finite-size corrections for the spanning-tree model under different boundary conditions
摘要：
我们表示的配分函数的生成树有限正方形格在五个不同的边界条件（自由，圆柱形，环形，莫比乌斯带，克莱因瓶）的一个主要的配分函数扭曲的边界条件。基于这些表达式，我们推导出每种情况下配分函数的对数的精确渐近展开式。对于不同的边界条件，我们还建立了几组与生成树配分函数有关的恒等式。我们还解释了一个明显的差异之间的对数修正项的自由能的二维生成树模型与周期性和自由边界条件和共形场论的预测。在自由边界条件下，我们得到了与共形场论预言完全一致的生成树角自由能。
英文摘要：
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.
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