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关于二聚体模型的课堂讲稿-Lecture notes on the dimer model

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文件编号:5132
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标题(title):Lecture notes on the dimer model
关于二聚体模型的课堂讲稿
作者(author):Fabio Lucio Toninelli
出版社(publisher):
大小(size):739 kB (756751 bytes)
格式(extension):pdf
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Table of contents :
1. Perfect matchings on bipartite planar graphs......Page 2
1.1. Height function......Page 3
2.1. Counting perfect matchings: The bipartite case......Page 5
2.3. Existence of a Kasteleyn weighting......Page 9
2.4. Counting perfect matchings in the bipartite, non-planar case: periodic boundary conditions......Page 11
2.5. Counting perfect matchings: The planar, non-bipartite case......Page 17
2.6. Random perfect matchings: correlation functions......Page 19
3.1. Free energy......Page 21
3.2. Computing the free energy on the torus......Page 22
3.3. Infinite-volume correlation functions......Page 26
3.4. Large distance behavior of K-1......Page 31
3.5. General bipartite, periodic toroidal graphs......Page 34
3.6. Phase structure: liquid, frozen and gaseous phases......Page 37
4.1. Height change and Legendre duality......Page 39
4.2. Macroscopic shape......Page 45
5. Height flucuations in ``liquid'' phases, and massless Gaussian Field......Page 48
6.1. Ising and dimers......Page 56
6.3. Temperley's bijection and spanning trees......Page 61
A.1. Proof of Lemma 3.7......Page 62
A.3. Proof of Lemma 3.9......Page 63
References......Page 65

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