Holographic free energy and thermodynamic geometry

Abstract

We analytically obtain the free energy and thermodynamic geometry of holographic superconductors in $2+1$-dimensions. The gravitational theory in the bulk dual to this $2+1$-dimensional strongly coupled theory lives in the $3+1$-dimensions and is that of a charged $AdS$ black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method.

arXiv comment13 pages Latex

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Cited by in corpus (6)

• Non-linear effects on the holographic free energy and thermodynamic geometry
• Effect of magnetic field on holographic insulator/superconductor phase transition in higher dimensional Gauss-Bonnet gravity
• Holographic insulator/superconductor phase transition in higher dimensional Gauss-Bonnet gravity
• Noncommutative effects of charged black hole on holographic superconductors
• Effects of massive gravity on $s$-wave holographic superconductor
• Holographic insulator/superconductor phase transition by matching method and thermodynamic geometry