Shirsendu Dey, Arindam Lala
In this paper, taking advantages of AdS/CFT correspondence, we have systematically studied the onset of holographic s-wave condensate in the planar Gauss-Bonnet-AdS black hole background. In the probe limit, we have considered two different kinds of non-linear electrodynamics, namely the exponential and logarithmic form of electrodynamics, in the matter action which may be considered as higher derivative corrections to the gauge fields in the usual Maxwell electrodynamics. Performing explicit analytic computations we have been able to determine several quantities characterising the holographic condensates for the two cases. We have determined the critical exponent associated with the order parameter of condensation and inferred that the condensates actually exhibit mean field behaviour and undergo a second order phase transition in going from normal to superconducting phase. We have also investigated the response of the condensates in an external magnetic field. We have shown that, in both cases, the non-linear as well as the higher curvature corrections tend to make the condensation harder. Interestingly, the external magnetic field also has similar effects on the holographic condensates. As a next step, we have performed a comparative study of the two non-linear electrodynamics and shown that the exponential electrodynamics has stronger effects on the formation of the scalar hair. We observe that our results agree well with those obtained numerically by Z. Zhao et. al. [Nucl. Phys. B 871 [FS] (2013) 98].
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http://arxiv.org/abs/1306.5137
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