"Integrable perturbation of Yang-Lee model"의 두 판 사이의 차이

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imported>Pythagoras0
 
imported>Pythagoras0
1번째 줄: 1번째 줄:
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==introduction==
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* S-matrix describes the infrared data of the model
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* it is important to check that the UV limit of the model coincides with the conformal field theory that was originally perturbed
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* TBA is a method which provides such a check
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 +
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==perturbed action==
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* $\mathcal{A}_{SLYM}=\mathcal{A}_{M_{2,5}}+i \lambda \int d^2x \varphi(x)$
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* $M=(2.642944662\cdots) \lambda^{5/12}$ where $M$ is the single particle mass
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* http://www.wolframalpha.com/input/?i=2.642944662
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* spin of conserved charges : 1,5,7,11,13,17,19, ...
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 +
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==S-matrix==
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* 1 particle
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* S-matrix
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$$
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S_{11}(\theta)=\tanh \left(\frac{1}{2} \left(\theta -\frac{2 i \pi }{3}\right)\right) \coth \left(\frac{1}{2} \left(\theta +\frac{2 i \pi }{3}\right)\right)
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$$
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* 커널
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$$
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\phi_{11}(\theta)=-i\frac{d}{d\theta}\log S_{11}(\theta)=\sqrt{3} \left(\frac{1}{2 \cosh (\theta )+1}+\frac{1}{2 \cosh (\theta )-1}\right)
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$$
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==TBA analysis==
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*
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$$
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N=\frac{1}{2\pi}\int_{-\infty}^{\infty}\phi_{11}(\theta)=1
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$$
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==related items==
 
==related items==
 
* [[Integrable perturbations of Ising model‎]]
 
* [[Integrable perturbations of Ising model‎]]
 
* [[(2,5) minimal Yang-Lee model]]
 
* [[(2,5) minimal Yang-Lee model]]
 
* [[Massive integrable perturbations of CFT and quasi-particles]]
 
* [[Massive integrable perturbations of CFT and quasi-particles]]
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==computational resource==
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* https://docs.google.com/file/d/0B8XXo8Tve1cxVlhNYUY5d3RZMWs/edit
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==articles==
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* 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
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* 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
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* 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

2013년 3월 12일 (화) 16:21 판

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

$$ N=\frac{1}{2\pi}\int_{-\infty}^{\infty}\phi_{11}(\theta)=1 $$


related items


computational resource


articles

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