"Dimer model"의 두 판 사이의 차이
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| 117번째 줄: | 117번째 줄: | ||
<h5>expositions</h5> | <h5>expositions</h5> | ||
| + | * Dimer Problems<br> | ||
| + | ** Richard Kenyon, 2005 | ||
* [http://arxiv.org/abs/math/0312099 Gaussian free fields for mathematicians]<br> | * [http://arxiv.org/abs/math/0312099 Gaussian free fields for mathematicians]<br> | ||
** Scott Sheffield, 2003 | ** Scott Sheffield, 2003 | ||
* [http://arxiv.org/abs/math/0310326 An introduction to the dimer model]<br> | * [http://arxiv.org/abs/math/0310326 An introduction to the dimer model]<br> | ||
** Richard Kenyon, 2003 | ** Richard Kenyon, 2003 | ||
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* http://members.unine.ch/beatrice.detiliere/Cours/Ecole_Doctorale.pdf<br> | * http://members.unine.ch/beatrice.detiliere/Cours/Ecole_Doctorale.pdf<br> | ||
* [http://pictor.math.uqam.ca/%7Eplouffe/OEIS/archive_in_pdf/domino.pdf Dimers and Dominos]<br> | * [http://pictor.math.uqam.ca/%7Eplouffe/OEIS/archive_in_pdf/domino.pdf Dimers and Dominos]<br> | ||
** James Propp, 1992 | ** James Propp, 1992 | ||
| + | * pictures<br> | ||
| + | ** http://research.microsoft.com/en-us/um/people/cohn/randomtilings.html | ||
2010년 10월 6일 (수) 08:06 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=
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://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
experts on the field