Holographic free energy and thermodynamic geometry

TL;DR

This paper analytically derives the free energy and thermodynamic geometry of 2+1-dimensional holographic superconductors using gauge/gravity duality, providing insights into phase transitions and critical temperatures.

Contribution

It introduces an analytical approach to compute free energy and thermodynamic geometry of holographic superconductors, linking divergence of scalar curvature to critical temperature.

Findings

Critical temperature matches between free energy and thermodynamic geometry methods.

Divergence of thermodynamic scalar curvature indicates phase transition.

Analytical expressions for free energy in holographic superconductor model.

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.