反铁磁 Potts 模型的转移矩阵与配分函数零点：V. 方格晶格色多项式的进一步结果
统计力学
2015-10-08 v2 高能物理 - 格点
组合数学
摘要
我们推导了具有自由边界条件和圆柱边界条件的方格晶格 Potts 模型转移矩阵的一些新结构结果。特别是，我们得到了任意宽度 m 下转移矩阵中主导（在大 |q| 时）对角元（作为特殊一维聚合物模型的解）的显式闭式表达式。我们还得到了零温反铁磁体（即色多项式）体自由能和表面（分别对应角）自由能的大 q 展开，精度分别达到 q^{-47} 和 q^{-46}。最后，我们计算了宽度 9 <= m <= 12 且具有自由边界条件的条带的色根，并大致确定了极限曲线的位置。
引用
@article{arxiv.0711.1738,
title = {Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial},
author = {Jesus Salas and Alan D. Sokal},
journal= {arXiv preprint arXiv:0711.1738},
year = {2015}
}
备注
111 pages (LaTeX2e). Includes tex file, three sty files, and 19 Postscript figures. Also included are Mathematica files data_CYL.m and data_FREE.m. Many changes from version 1: new material on series expansions and their analysis, and several proofs of previously conjectured results. Final version to be published in J. Stat. Phys