Analytical Computation of Critical Exponents in Several Holographic Superconductors

TL;DR

This paper analytically investigates the critical exponents of various holographic superconductors, revealing that fundamental symmetries, rather than detailed parameters, determine their universal mean-field behavior, and explores conditions for non-mean-field deviations.

Contribution

It provides an analytical approach to compute critical exponents in holographic superconductors, highlighting the role of symmetries in universal phase transition properties.

Findings

Universal mean-field critical exponent 1/2 observed in most holographic superconductors.

Non-mean-field behavior with a different exponent 1 identified in extended models.

Symmetries of the bulk gravity theory are key to universal critical behavior.

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.