Discrete Mathematics in Statistical Physics - Introductory Lectures
Discrete Mathematics in Statistical Physics - Introductory Lectures
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统计物理中的离散数学 - 入门讲座
DOI：
10.1007/978-3-8348-9329-1
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
M. Loebl
中科院分区：
文献类型：
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作者：
M. Loebl
这些课堂讲稿的目的是简要地描述一些基本概念交错离散数学，统计物理学和纽结理论。我试图强调“组合常识”作为主要方法。没有尝试完整性。这本书应该是学数学和物理的学生都能读得懂的。我从以前的书籍和离散数学，统计物理，纽结理论和其他人的论述中受益，即[B1]，[BRJ]，[BB]，[J1]，[KG]，[LL]，[MN]，[MJ]，[MT]，[S 0]，[S3]，[SM]，[WFY]，[WD]，[KSV]。书中所包含的大部分材料都是介绍性的，没有提到原始来源。这本书是我的编辑马丁艾格纳的一个想法。我要感谢他的支持和帮助。许多同事帮助我完成了这本书。Mihyun Kang，Jirka Matoušek，Iain Moffatt，Jarik Nešetril，Dominic Welsh和Christian Krattenthaler阅读了早期版本，如果没有他们的广泛评论，这本书可能不会存在。我就书中讨论的几个主题进行了富有启发性的讨论，特别是与马丁·克拉扎尔、罗曼·科特克茨、昂德雷·潘格拉茨、格雷戈尔·马斯鲍姆、泽维尔·维耶诺特和乌利·瓦格纳的讨论。Marcos Kiwi温柔地教我如何画画，Winfried Hochstaettler画了一张，挽救了整个项目;我相信你能发现它。这本书的大部分是在我访问期间写的，在整个2006年，在数学学院和数学建模中心，智利大学。我要感谢那里的同事的盛情款待，并衷心感谢CONICYT通过项目Anillo en Redes，ACT-08提供的支持。当然，在我写这本书的过程中，最重要的因素是我所在的应用数学系和布拉格查尔斯大学理论计算机科学研究所的创造性环境。书中的一些定理和观察似乎没有证明。通常一个指针是指向一本书（优先）或一篇论文，在那里可以找到证明。如果没有指针，那么我相信（可能是错误的），应该可以用一种简单而不太复杂的方式证明这个陈述。鼓励读者把这样的证明写下来作为练习。前五章集中介绍离散数学。第六章和第七章专门讨论配分函数，第八章是纽结理论的介绍。最后一章介绍了两种求解二维Ising问题和二维二聚体问题的组合技术。
The purpose of these lecture notes is to briefly describe some of the basic concepts interlacing discrete mathematics, statistical physics and knot theory. I tried to emphasize a’combinatorial common sense’as the main method. No attempt of completeness was made. The book should be accessible to the students of both mathematics and physics. I profited from previous books and expositions on discrete mathematics, statistical physics, knot theory and others, namely [B1],[BRJ],[BB],[J1],[KG],[LL],[MN],[MJ],[MT],[S0],[S3],[SM],[WFY],[WD],[KSV]. Most of the material contained in the book is introductory and appears without a reference to the original source. This book has been an idea of my editor Martin Aigner. I would like to thank to him for his support and help. Many other colleagues helped me with the book. Mihyun Kang, Jirka Matoušek, Iain Moffatt, Jarik Nešetril, Dominic Welsh and Christian Krattenthaler read earlier versions, and without their extensive comments the book would probably not exist. I had enlightening discussions on several topics discussed in the book, in particular with Martin Klazar, Roman Kotecký, Ondrej Pangrác, Gregor Masbaum, Xavier Viennot and Uli Wagner. Marcos Kiwi saved the whole project by gently teaching me how to draw pictures amd Winfried Hochstaettler drew one; I am sure you will be able to detect it. Large part of the book was written during my visit, in the whole year 2006, at the School of Mathematics and the Centro Modelamiento Matematico, Universidad de Chile. I want to thank my colleagues there for wonderful hospitality, and gratefully acknowledge the support of CONICYT via project Anillo en Redes, ACT-08. But of course, the seminal ingredient in the process of making the book was the creative environment of my home department of applied mathematics and the institute of theoretical computer science at the Charles University, Prague. Some theorems and observations in the book appear without a proof. Usually a pointer is given to a book (preferentially) or to a paper where a proof can be found. If no pointer is given, then I believe (possibly mistakenly) that it should be possible to prove the statement in an elementary and not very complicated way. The reader is encouraged to write down such proofs as exercises. The first five chapters concentrate on the introductory discrete mathematics. Chapters six and seven are devoted to the partition functions, and chapter eight is an introduction to the theory of knots. The last chapter describes two combinatorial technics which solve the 2D Ising and dimer problems.