"Transfer matrix in statistical mechanics"의 두 판 사이의 차이
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==expositions== | ==expositions== | ||
| − | + | * “The Kramers-Wannier Transfer Matrix.” 1980. In The Ruelle-Araki Transfer Operator in Classical Statistical Mechanics, 13–39. Lecture Notes in Physics 123. Springer Berlin Heidelberg. http://link.springer.com/chapter/10.1007/BFb0017921. | |
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[[분류:개인노트]] | [[분류:개인노트]] | ||
[[분류:integrable systems]] | [[분류:integrable systems]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
2013년 6월 30일 (일) 05:19 판
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
- 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
Bethe ansatz
- Bethe ansatz equation is used to find the eigenvectors and eigenvalues of the transfer matrix
transfer matrix of the six-vertex model
expositions
- “The Kramers-Wannier Transfer Matrix.” 1980. In The Ruelle-Araki Transfer Operator in Classical Statistical Mechanics, 13–39. Lecture Notes in Physics 123. Springer Berlin Heidelberg. http://link.springer.com/chapter/10.1007/BFb0017921.