"Transfer matrix in statistical mechanics"의 두 판 사이의 차이
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imported>Pythagoras0 |
Pythagoras0 (토론 | 기여) |
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| (사용자 2명의 중간 판 12개는 보이지 않습니다) | |||
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==introduction== | ==introduction== | ||
| − | * transfer matrix is builtup from matrices of | + | * transfer matrix is builtup from matrices of Boltzmann weights |
| − | * trace of | + | * trace of [[Monodromy matrix]] is the transfer matrix |
* finding eigenvalues and eigenvectors of transfer matrix is crucial | * finding eigenvalues and eigenvectors of transfer matrix is crucial | ||
| − | + | * partition function = trace of power of transfer matrices | |
| − | * partition function = | + | * so the partition function is calculated in terms of the eigenvalues of the transfer matrix |
| − | * so | ||
* then the problem of solving the model is reduced to the computation of this trace | * 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 | |
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* [[Six-vertex model and Quantum XXZ Hamiltonian]] | * [[Six-vertex model and Quantum XXZ Hamiltonian]] | ||
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==related items== | ==related items== | ||
* [[S-matrix or scattering matrix]] | * [[S-matrix or scattering matrix]] | ||
| − | + | * [[1d Ising model]] | |
| − | + | * [[Ising model on rectangular lattice]] | |
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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]] | ||
| + | [[분류:migrate]] | ||
2020년 12월 28일 (월) 05:07 기준 최신판
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.