Free energy of a Lovelock holographic superconductor

TL;DR

This paper derives an exact, analytic formula for the free energy of a holographic superconductor modeled by Lovelock gravity with scalar hair, incorporating backreaction effects and enabling phase transition analysis.

Contribution

It provides a new analytic expression for the free energy of Lovelock holographic superconductors, including backreaction, broadening the understanding of phase transitions in these models.

Findings

Exact free energy formula derived for Lovelock holographic superconductor.

Inclusion of backreaction effects in the thermodynamic analysis.

Framework for analyzing second order phase transitions via free energy discontinuities.

Abstract

We study thermodynamics of black hole solutions in Lanczos-Lovelock AdS gravity in d+1 dimensions coupled to nonlinear electrodynamics and a Stueckelberg scalar field. This class of theories is used in the context of gauge/gravity duality to describe a high-temperature superconductor in d dimensions. Larger number of coupling constants in the gravitational side is necessary to widen a domain of validity of physical quantities in a dual QFT. We regularize the gravitational action and find the finite conserved quantities for a planar black hole with scalar hair. Then we derive the quantum statistical relation in the Euclidean sector of the theory, and obtain the exact formula for the free energy of the superconductor in the holographic quantum field theory. Our result is analytic and it includes the effects of backreaction of the gravitational field. We further discuss on how this formula could be used to analyze second order phase transitions through the discontinuities of the free energy, in order to classify holographic superconductors in terms of the parameters in the theory.