Dimer model

introduction

• Gaussian free field [1]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

 

 

 

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

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

related items[[Schramm–Loewner evolution (SLE)|]]

• basic thermodynamics & statistical mechanics
• Schramm–Loewner evolution (SLE)

 

 

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

• [2]http://arxiv.org/abs/math/0310326
  
  • 2003
• Lozenge Tiling
• pictures
  
  • http://research.microsoft.com/en-us/um/people/cohn/randomtilings.html
• 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
• 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)

• http://mathoverflow.net/search?q=dimer
• http://mathoverflow.net/search?q=

 

 

blogs

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=dimer+model
• http://ncatlab.org/nlab/show/HomePage

 

 

experts on the field

• http://arxiv.org/

 

 

links

• http://ipht.cea.fr/statcomb2009/dimers/abstracts.html
• Detexify2 - LaTeX symbol classifier
• 수식표현 안내
• The On-Line Encyclopedia of Integer Sequences
• http://functions.wolfram.com/