"Transfer matrix in statistical mechanics"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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* trace of monodromy matrix is the transfer matrix | * 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 | ||
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* partition function = trace of power of transfer matrices | * partition function = trace of power of transfer matrices | ||
* so the partition function is calculated in terms of the eigenvalues of the transfer matrix | * so the partition function is calculated in terms of the eigenvalues of the transfer matrix | ||
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| − | == | + | ==Bethe ansatz== |
| − | * [[ | + | * [[Bethe ansatz]] equation is used to find the eigenvectors and eigenvalues of the transfer matrix |
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| 25번째 줄: | 19번째 줄: | ||
==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== | ||
2013년 2월 19일 (화) 13:10 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
- Anon.1980. The Ruelle-Araki Transfer Operator in Classical Statistical Mechanics. Vol. 123. Berlin/Heidelberg: Springer-Verlag.[1]http://www.springerlink.com/content/f12j034740601kjx/.