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摘要翻译：
对于自由边界条件和圆柱边界条件下的平方格Potts模型的转移矩阵，我们得到了一些新的结构结果。特别地，我们得到了在任意宽度m下，传递矩阵中主要（大致q）对角入口的显式闭式表达式，作为一个特殊的一维聚合物模型的解。我们还得到了零温反铁磁体(=色多项式）的体自由能和表面自由能的大q展开式(q^{-47}（q^{-46}）。最后，在自由边界条件下，计算了宽度为9<=m<=12的条带的色根，并粗略地确定了极限曲线。
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英文标题：
《Transfer Matrices and Partition-Function Zeros for Antiferromagnetic
Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial》
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作者：
Jesus Salas and Alan D. Sokal
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最新提交年份：
2009
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics 物理学
二级分类：High Energy Physics - Lattice 高能物理-晶格
分类描述：Lattice field theory. Phenomenology from lattice field theory. Algorithms for lattice field theory. Hardware for lattice field theory.
晶格场论。从晶格场论到现象学。格场论的算法。晶格场论硬件。
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一级分类：Mathematics 数学
二级分类：Combinatorics 组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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英文摘要：
We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47} (resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <= m <= 12 with free boundary conditions and locate roughly the limiting curves.
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PDF链接：
https://arxiv.org/pdf/711.1738
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