"Integrable perturbation of Yang-Lee model"의 두 판 사이의 차이
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imported>Pythagoras0 |
Pythagoras0 (토론 | 기여) |
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| (사용자 2명의 중간 판 4개는 보이지 않습니다) | |||
| 6번째 줄: | 6번째 줄: | ||
==perturbed action== | ==perturbed action== | ||
| − | * | + | * <math>\mathcal{A}_{SLYM}=\mathcal{A}_{M_{2,5}}+i \lambda \int d^2x \varphi(x)</math> |
| − | * | + | * <math>M=(2.642944662\cdots) \lambda^{5/12}</math> where <math>M</math> is the single particle mass |
* http://www.wolframalpha.com/input/?i=2.642944662 | * http://www.wolframalpha.com/input/?i=2.642944662 | ||
* spin of conserved charges : 1,5,7,11,13,17,19, ... | * spin of conserved charges : 1,5,7,11,13,17,19, ... | ||
| 15번째 줄: | 15번째 줄: | ||
* 1 particle | * 1 particle | ||
* S-matrix | * S-matrix | ||
| − | + | :<math> | |
S_{11}(\theta)=\tanh \left(\frac{1}{2} \left(\theta -\frac{2 i \pi }{3}\right)\right) \coth \left(\frac{1}{2} \left(\theta +\frac{2 i \pi }{3}\right)\right) | S_{11}(\theta)=\tanh \left(\frac{1}{2} \left(\theta -\frac{2 i \pi }{3}\right)\right) \coth \left(\frac{1}{2} \left(\theta +\frac{2 i \pi }{3}\right)\right) | ||
| − | + | </math> | |
* 커널 | * 커널 | ||
| − | + | :<math> | |
\phi_{11}(\theta)=-i\frac{d}{d\theta}\log S_{11}(\theta)=\sqrt{3} \left(\frac{1}{2 \cosh (\theta )+1}+\frac{1}{2 \cosh (\theta )-1}\right) | \phi_{11}(\theta)=-i\frac{d}{d\theta}\log S_{11}(\theta)=\sqrt{3} \left(\frac{1}{2 \cosh (\theta )+1}+\frac{1}{2 \cosh (\theta )-1}\right) | ||
| − | + | </math> | |
==TBA analysis== | ==TBA analysis== | ||
* | * | ||
| − | + | :<math> | |
N=\frac{1}{2\pi}\int_{-\infty}^{\infty}\phi_{11}(\theta)=1 | N=\frac{1}{2\pi}\int_{-\infty}^{\infty}\phi_{11}(\theta)=1 | ||
| − | + | </math> | |
| 43번째 줄: | 43번째 줄: | ||
==articles== | ==articles== | ||
| + | * Bianchini, Davide, Olalla A. Castro-Alvaredo, and Benjamin Doyon. ‘Entanglement Entropy of Non-Unitary Integrable Quantum Field Theory’. arXiv:1502.03275 [cond-Mat, Physics:hep-Th], 11 February 2015. http://arxiv.org/abs/1502.03275. | ||
* Fateev, V. A. 1994. “The Exact Relations Between the Coupling Constants and the Masses of Particles for the Integrable Perturbed Conformal Field Theories.” Physics Letters. B 324 (1): 45–51. doi:10.1016/0370-2693(94)00078-6. http://www.sciencedirect.com/science/article/pii/0370269394000786 | * Fateev, V. A. 1994. “The Exact Relations Between the Coupling Constants and the Masses of Particles for the Integrable Perturbed Conformal Field Theories.” Physics Letters. B 324 (1): 45–51. doi:10.1016/0370-2693(94)00078-6. http://www.sciencedirect.com/science/article/pii/0370269394000786 | ||
* Zamolodchikov, Al.B. 1990. “Thermodynamic Bethe Ansatz in Relativistic Models: Scaling 3-state Potts and Lee-Yang Models.” Nuclear Physics B 342 (3) (October 8): 695–720. doi:10.1016/0550-3213(90)90333-9. http://www.sciencedirect.com/science/article/pii/0550321390903339 | * Zamolodchikov, Al.B. 1990. “Thermodynamic Bethe Ansatz in Relativistic Models: Scaling 3-state Potts and Lee-Yang Models.” Nuclear Physics B 342 (3) (October 8): 695–720. doi:10.1016/0550-3213(90)90333-9. http://www.sciencedirect.com/science/article/pii/0550321390903339 | ||
* Cardy, John L., and G. Mussardo. 1989. “S-matrix of the Yang-Lee Edge Singularity in Two Dimensions.” Physics Letters B 225 (3) (July 20): 275–278. doi:10.1016/0370-2693(89)90818-6. http://www.sciencedirect.com/science/article/pii/0370269389908186 | * Cardy, John L., and G. Mussardo. 1989. “S-matrix of the Yang-Lee Edge Singularity in Two Dimensions.” Physics Letters B 225 (3) (July 20): 275–278. doi:10.1016/0370-2693(89)90818-6. http://www.sciencedirect.com/science/article/pii/0370269389908186 | ||
| + | [[분류:migrate]] | ||
2020년 11월 16일 (월) 11:02 기준 최신판
introduction
- S-matrix describes the infrared data of the model
- it is important to check that the UV limit of the model coincides with the conformal field theory that was originally perturbed
- TBA is a method which provides such a check
perturbed action
- \(\mathcal{A}_{SLYM}=\mathcal{A}_{M_{2,5}}+i \lambda \int d^2x \varphi(x)\)
- \(M=(2.642944662\cdots) \lambda^{5/12}\) where \(M\) is the single particle mass
- http://www.wolframalpha.com/input/?i=2.642944662
- spin of conserved charges : 1,5,7,11,13,17,19, ...
S-matrix
- 1 particle
- S-matrix
\[ S_{11}(\theta)=\tanh \left(\frac{1}{2} \left(\theta -\frac{2 i \pi }{3}\right)\right) \coth \left(\frac{1}{2} \left(\theta +\frac{2 i \pi }{3}\right)\right) \]
- 커널
\[ \phi_{11}(\theta)=-i\frac{d}{d\theta}\log S_{11}(\theta)=\sqrt{3} \left(\frac{1}{2 \cosh (\theta )+1}+\frac{1}{2 \cosh (\theta )-1}\right) \]
TBA analysis
\[ N=\frac{1}{2\pi}\int_{-\infty}^{\infty}\phi_{11}(\theta)=1 \]
- Integrable perturbations of Ising model
- (2,5) minimal Yang-Lee model
- Massive integrable perturbations of CFT and quasi-particles
computational resource
articles
- Bianchini, Davide, Olalla A. Castro-Alvaredo, and Benjamin Doyon. ‘Entanglement Entropy of Non-Unitary Integrable Quantum Field Theory’. arXiv:1502.03275 [cond-Mat, Physics:hep-Th], 11 February 2015. http://arxiv.org/abs/1502.03275.
- Fateev, V. A. 1994. “The Exact Relations Between the Coupling Constants and the Masses of Particles for the Integrable Perturbed Conformal Field Theories.” Physics Letters. B 324 (1): 45–51. doi:10.1016/0370-2693(94)00078-6. http://www.sciencedirect.com/science/article/pii/0370269394000786
- Zamolodchikov, Al.B. 1990. “Thermodynamic Bethe Ansatz in Relativistic Models: Scaling 3-state Potts and Lee-Yang Models.” Nuclear Physics B 342 (3) (October 8): 695–720. doi:10.1016/0550-3213(90)90333-9. http://www.sciencedirect.com/science/article/pii/0550321390903339
- Cardy, John L., and G. Mussardo. 1989. “S-matrix of the Yang-Lee Edge Singularity in Two Dimensions.” Physics Letters B 225 (3) (July 20): 275–278. doi:10.1016/0370-2693(89)90818-6. http://www.sciencedirect.com/science/article/pii/0370269389908186