"Dimer model"의 두 판 사이의 차이
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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 | ||
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| + | <h5> </h5> | ||
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| + | # detk[m_, n_] :=<br> N[Product[<br> Product[2 Cos[(Pi*l)/(m + 1)] + 2 I*Cos[(Pi*k)/(n + 1)], {k, 1,<br> n}], {l, 1, m}], 10]<br> detk[4, 4] | ||
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* <br> | * <br> | ||
** Richard Kenyon, The Annals of Probability Vol. 28, No. 2 (Apr., 2000), pp. 759-795 | ** Richard Kenyon, The Annals of Probability Vol. 28, No. 2 (Apr., 2000), pp. 759-795 | ||
| − | * | + | * [http://dx.doi.org/10.1007/BF02392811 The asymptotic determinant of the discrete Laplacian]<br> |
| − | ** Richard Kenyon, Acta Mathematica Volume 185, Number 2, 239-286 | + | ** 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 | * 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.ams.org/mathscinet | ||
| 143번째 줄: | 147번째 줄: | ||
* http://pythagoras0.springnote.com/ | * http://pythagoras0.springnote.com/ | ||
* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html] | * [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html] | ||
| − | * http://dx.doi.org/10. | + | * http://dx.doi.org/10.1007/BF02392811 |
2010년 10월 2일 (토) 14:54 판
introduction
- massless Gaussian free field http://arxiv.org/abs/math/0312099
- 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
- 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]
detk[4, 4]
memo
http://www.umich.edu/~mctp/SciPrgPgs/events/2006/2006glsc/talks/hanany.pdf
Dimers and Dominos
http://pictor.math.uqam.ca/~plouffe/OEIS/archive_in_pdf/domino.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
- [1]http://arxiv.org/abs/math/0310326
- 2003
- Lozenge Tiling
- pictures
- http://members.unine.ch/beatrice.detiliere/Cours/Ecole_Doctorale.pdf
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