Transfer matrix in statistical mechanics

introduction

• transfer matrix is builtup from matrices of  Boltzmann weights
• trace of monodromy matrix is the transfer matrix
• finding eigenvalues and eigenvectors of transfer matrix is crucial
• Bethe ansatz equation is used to find the eigenvectors and eigenvalues of the transfer matrix
• partition function = trace of power of transfer matrices
• so the partition function  is calculated in terms of the eigenvalues of the transfer matrix

• then the problem of solving the model is reduced to the computation of this trace
  

transfer matrix of the 1D Ising model

 * 1d Ising model

transfer matrix of the 2D Ising model

• Ising model on rectangular lattice

transfer matrix of the six-vertex model

• Six-vertex model and Quantum XXZ Hamiltonian

 

history

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

 

 

related items

• S-matrix or scattering matrix

 

encyclopedia

• http://en.wikipedia.org/wiki/
• http://www.scholarpedia.org/
• http://www.proofwiki.org/wiki/

 

 

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

• Anon.1980. The Ruelle-Araki Transfer Operator in Classical Statistical Mechanics. Vol. 123. Berlin/Heidelberg: Springer-Verlag.[1]http://www.springerlink.com/content/f12j034740601kjx/.
   
   

 

articles

 

• http://www.ams.org/mathscinet
• [2]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/

 

 

question and answers(Math Overflow)

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

 

 

blogs

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

 

 

experts on the field

• http://arxiv.org/

 

 

links

• Detexify2 - LaTeX symbol classifier
• 수식표현 안내
• The On-Line Encyclopedia of Integer Sequences
• http://functions.wolfram.com/