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Analytical computation of critical exponents in several holographic superconductors

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Abstract

It is very interesting that all holographic superconductors, such as s-wave, p-wave and d-wave holographic superconductors, show the universal mean-field critical exponent 1/2 at the critical temperature, just like Gindzburg-Landau (G-L) theory for second order phase transitions. Now it is believed that the universal critical exponents appear because the dual gravity theory is classic in the large N limit. However, even in the large N limit there is an exception called “non-mean-field theory”: an extension of the s-wave model with a cubic term of the charged scalar field shows a different critical exponent 1. In this paper, we try to use analytical methods to obtain the critical exponents for these models to see how the properties of the gravity action decides the appearance of the mean-field behaviors. It will be seen that just like the G-L theory, it is the fundamental symmetries rather than the detailed parameters of the bulk theory that lead to the universal properties of the holographic superconducting phase transition. The feasibility of the called “non-mean-field theory” is also discussed.

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Authors and Affiliations

  1. Department of Physics, Nanjing University, Nanjing, 210093, China

    Hua-Bi Zeng & Hong-Shi Zong

  2. Key Laboratory of Frontiers in Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China

    Xin Gao

  3. Center for Statistical and Theoretical Condensed Matter Physics & Department of Physics, Zhejiang Normal University, Jinhua, 321004, China

    Yu Jiang

  4. Joint Center for Particle, Nuclear Physics and Cosmology, Nanjing University, Nanjing, 210093, China

    Hong-Shi Zong

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  1. Hua-Bi Zeng
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  2. Xin Gao
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  3. Yu Jiang
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  4. Hong-Shi Zong
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Correspondence to Hua-Bi Zeng.

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Zeng, HB., Gao, X., Jiang, Y. et al. Analytical computation of critical exponents in several holographic superconductors. J. High Energ. Phys. 2011, 2 (2011). https://doi.org/10.1007/JHEP05(2011)002

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  • DOI: https://doi.org/10.1007/JHEP05(2011)002

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