Analytical Computation of Critical Exponents in Several Holographic Superconductors

Understand

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.