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arXiv 2009.12016cond-mat.stat-mechphysics.hist-ph
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数学物理中的Legerdemain:二维伊辛模型的配分函数推导中的结构、技巧和缺陷以及物质稳定性的证明

Legerdemain in Mathematical Physics: Structure, Tricks, and Lacunae in Derivations of the Partition Function of the Two-Dimensional Ising Model and in Proofs of The Stability of Matter

Martin H. Krieger

摘要:

我们回顾各种推导的配分函数的二维伊辛模型的铁磁性和物质的稳定性的证明,注意段落之间似乎有一个空白的步骤或结构的论点是不是那么简单。作者不能包括所有的中间步骤,但有时大多数读者,尤其是学生会对这样的过渡感到困惑。此外,仔细考虑这样的空白点有趣的物理学,而不仅仅是数学技术。此外,在阅读原始论文时,物理论点的结构可能会被技术动作所掩盖。在其他人随后的论文中,推导过程的改进可能会更清晰,更有动力。但是,关于如何阅读一些原始论文和后续论文的书面和出版物非常少,但学生和他们的老师通常会从这样的指导中受益。我应该指出,下面的大部分讨论将受益于这些文件。

英文摘要:

We review various derivations of the partition function of the two-dimensional Ising Model of ferromagnetism and proofs of the stability of matter, paying attention to passages where there would appear to be a lacuna between steps or where the structure of the argument is not so straightforward. Authors cannot include all the intermediate steps, but sometimes most readers and especially students will be mystified by such a transition. Moreover, careful consideration of such lacunae points to interesting physics and not only mathematical technology. Also, when reading the original papers, the structure of the physics argument may be buried by the technical moves. Improvements in the derivations, in subsequent papers by others, may well be clearer and more motivated. But, there is remarkably little written and published about how to read some of the original papers, and the subsequent ones, yet students and their teachers would often benefit from such guidance. I should note that much of the discussion below will benefit from having those papers in front of you.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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