"Dimer model"의 두 판 사이의 차이
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| 1번째 줄: | 1번째 줄: | ||
<h5>introduction</h5> | <h5>introduction</h5> | ||
| − | * Gaussian free field | + | * Gaussian free field [http://arxiv.org/abs/math/0312099 ]http://arxiv.org/abs/math/0312099 |
| − | + | * relation to Bethe ansatz [http://staff.science.uva.nl/%7Enienhuis/tiles.pdf http://staff.science.uva.nl/~nienhuis/tiles.pdf] | |
| 13번째 줄: | 13번째 줄: | ||
* set of dimer configurations | * set of dimer configurations | ||
* partition function | * partition function | ||
| + | * Kasteleyn matrix | ||
2010년 10월 1일 (금) 18:42 판
introduction
- Gaussian free field [1]http://arxiv.org/abs/math/0312099
- relation to Bethe ansatz http://staff.science.uva.nl/~nienhuis/tiles.pdf
basic notions
- dimer configurations
- set of dimer configurations
- partition function
- Kasteleyn matrix
physics motivation
Dimer configuration can be considered as the covering of the graph by pairs of fermions connected by an edge
Termperley equivalence
spanning trees on \gamma rooted at x
Dimers on D(\gamma)
Domino tiling and height function
bipartite graph
weight systems
define a weight function on the edges of the graph \gamma
history
encyclopedia
- http://en.wikipedia.org/wiki/Domino_tiling
- http://en.wikipedia.org/wiki/Lozenge
- http://en.wikipedia.org/wiki/Gaussian_free_field
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
expositions
- [2]http://arxiv.org/abs/math/0310326
- 2003
- Lozenge Tiling
- pictures
- http://members.unine.ch/beatrice.detiliere/Cours/Ecole_Doctorale.pdf
articles
- Dimers, Tilings and Trees
- 2000
- Kasteleyn, P. W. (1961), "The statistics of dimers on a lattice. I. The number of dimer arrangements on a quadratic lattice", Physica 27 (12): 1209–1225
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/10.1214/aop/1019160260
question and answers(Math Overflow)
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field