"Dimer model"의 두 판 사이의 차이
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| 21번째 줄: | 21번째 줄: | ||
<h5>physics motivation</h5> | <h5>physics motivation</h5> | ||
| − | Dimer configuration can be considered as the covering of the graph by pairs of fermions connected by an edge | + | * Dimer configuration can be considered as the covering of the graph by pairs of fermions connected by an edge |
| 29번째 줄: | 29번째 줄: | ||
<h5>Termperley equivalence</h5> | <h5>Termperley equivalence</h5> | ||
| − | spanning trees on \gamma rooted at x | + | * spanning trees on \gamma rooted at x |
| − | + | * Dimers on D(\gamma) | |
| − | Dimers on D(\gamma) | ||
| 39번째 줄: | 38번째 줄: | ||
<h5>Domino tiling and height function</h5> | <h5>Domino tiling and height function</h5> | ||
| − | bipartite graph | + | * bipartite graph |
| 47번째 줄: | 46번째 줄: | ||
<h5>weight systems</h5> | <h5>weight systems</h5> | ||
| − | define a weight function on the edges of the graph \gamma | + | * define a weight function on the edges of the graph \gamma |
| 110번째 줄: | 109번째 줄: | ||
* http://gigapedia.info/1/ | * http://gigapedia.info/1/ | ||
* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords= | * http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords= | ||
| + | |||
| + | |||
| + | |||
| + | <h5>links</h5> | ||
| + | |||
| + | * http://ipht.cea.fr/statcomb2009/dimers/abstracts.html | ||
| + | * [http://www.math.brown.edu/%7Erkenyon/papers/index.html http://www.math.brown.edu/~rkenyon/papers/index.html] | ||
| 136번째 줄: | 142번째 줄: | ||
<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles</h5> | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles</h5> | ||
| − | * | + | * http://arxiv.org/abs/cond-mat/0612573 |
* http://www.physics.neu.edu/faculty/wu%20files/pdf/Wu217_PRE74_020104%28R%29.pdf | * http://www.physics.neu.edu/faculty/wu%20files/pdf/Wu217_PRE74_020104%28R%29.pdf | ||
* [http://arxiv.org/abs/math/0310195 Dimers, Tilings and Trees] | * [http://arxiv.org/abs/math/0310195 Dimers, Tilings and Trees] | ||
| 175번째 줄: | 181번째 줄: | ||
| − | + | ||
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* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | * [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | ||
* [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내] | * [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내] | ||
* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] | * [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] | ||
* http://functions.wolfram.com/ | * http://functions.wolfram.com/ | ||
2010년 10월 13일 (수) 05:49 판
introduction
- relation to Bethe ansatz http://staff.science.uva.nl/~nienhuis/tiles.pdf
- domino tilings http://www-math.mit.edu/~rstan/transparencies/tilings3.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
mathematica code
- detk[m_, n_] :=
N[Product[
Product[2 Cos[(Pi*l)/(m + 1)] + 2 I*Cos[(Pi*k)/(n + 1)], {k, 1,
n}], {l, 1, m}], 10]
Z[m_, n_] := Round[Sqrt[Abs[detk[m, n]]]]
Z[8, 8]
memo
- http://www.umich.edu/~mctp/SciPrgPgs/events/2006/2006glsc/talks/hanany.pdf
- http://www.lif.univ-mrs.fr/~fernique/info/slides_csr.pdf
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
- Statistical mechanics
- 2010년 books and articles
- http://gigapedia.info/1/statistical+mechanics
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
links
- http://ipht.cea.fr/statcomb2009/dimers/abstracts.html
- http://www.math.brown.edu/~rkenyon/papers/index.html
expositions
- Dimer Problems
- Richard Kenyon, 2005
- Gaussian free fields for mathematicians
- Scott Sheffield, 2003
- An introduction to the dimer model
- Richard Kenyon, 2003
- http://members.unine.ch/beatrice.detiliere/Cours/Ecole_Doctorale.pdf
- Dimers and Dominos
- James Propp, 1992
- pictures
articles
- http://arxiv.org/abs/cond-mat/0612573
- http://www.physics.neu.edu/faculty/wu%20files/pdf/Wu217_PRE74_020104%28R%29.pdf
- Dimers, Tilings and Trees
- Richard Kenyon, The Annals of Probability Vol. 28, No. 2 (Apr., 2000), pp. 759-795
- The asymptotic determinant of the discrete Laplacian
- Richard Kenyon, Acta Mathematica Volume 185, Number 2, 239-286, 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/10.1007/BF02392811
question and answers(Math Overflow)
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage