Finite‐size scaling and phenomenological renormalization (invited)
Finite‐size scaling and phenomenological renormalization (invited)
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有限尺寸标度和唯象重整化（特邀）
DOI：
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发表时间：
1982
期刊：
影响因子：
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通讯作者：
Peter Nightingale
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文献类型：
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作者：
Peter Nightingale
近年来的研究表明，将有限尺寸标度理论与传递矩阵技术相结合，可以为研究临界行为提供强有力的工具。特别是，该方法已被用于研究二维统计力学和一维量子力学系统。我们从重整化群理论的一般观点来回顾有限尺寸标度理论，包括连续和一阶跃迁（包括具有离散和连续对称性的系统）。我们审查的应用程序，可以与精确的结果进行比较。这些模型包括Ising、巴克斯特和q态Potts模型以及带有缺陷线的Ising模型。各种其他应用，如量子系统，自避免随机行走，渗流，和Kosterlitz-无规跃迁简要回顾。反铁磁三态Potts模型中的Kosterlitz无相变和临界扇将以更长的篇幅讨论。
Research in recent years has shown that combining finite‐size scaling theory with the transfer matrix technique yields a powerful tool for the investigation of critical behavior. In particular, the method has been used to study two‐dimensional statistical mechanical and one‐dimensional quantum mechanical systems. We review finite‐size scaling theory from the general point of view of renormalization group theory for both continuous and first‐order transitions (both for systems with discrete and continuous symmetries). We review applications where a comparison with exact results can be made. These include the Ising, Baxter, and q‐state Potts models and the Ising model with a defect line. Various other applications such as quantum systems, the self‐avoiding random walk, percolation, and Kosterlitz‐Thouless transitions are briefly reviewed. The Kosterlitz‐Thouless transitions and the critical fan in the antiferromagnetic 3‐state Potts model are discussed at somewhat greater length.