AI 中文总结
本文推导了有限尺寸二维矩形伊辛模型边界行两自旋关联函数的精确表达式，验证其与前人热力学极限下的表达式形式一致，还分析了尺寸、极限顺序等对关联函数的影响。
AI 中文摘要
我们给出了有限尺寸且含周期-自由边界条件的二维矩形伊辛模型边界行中两个自旋之间关联函数的精确表达式，并讨论了所得精确表达式的若干性质。明确展示了伊辛模型的基本性质：随着温度降低会出现长程有序；热力学极限下的关联函数表达式取决于对两个参数L和N取极限的顺序；借助图示说明了不同尺寸对关联函数的影响。本文所讨论的热力学极限下的关联函数表达式已有前人给出，我们证明了本文所得表达式在形式上与前人提供的热力学极限下的表达式一致。
英文摘要
We present exact expressions of correlation functions between two spins in the boundary row of the two-dimensional rectangular Ising model with periodic-free boundary conditions and finite size. Some properties of exact expressions obtained are discussed. The fundamental property of the Ising model that the long range order emerge as the temperature decrease is shown clearly; expressions of the correlation functions in the thermodynamic limit varies depending on the order of taking limits of two parameters L and N; the impact of different sizes on correlation functions is illustrated with the aid of diagrams. Expressions of the correlation function discussed in this paper in the thermodynamic limit has been presented by previous researchers, and we prove that expressions obtained in this article is identical in form to expressions provided by previous researchers in the thermodynamic limit.
Comments35 pages, 7 figures,
