A Note on Holography and Phase Transitions

TL;DR

This paper explores the relationship between Landau theory and holography in phase transitions, providing analytical solutions that approximate numerical results in anti-de Sitter backgrounds.

Contribution

It introduces simple analytical approximations for holographic phase transitions, connecting Landau theory with holographic models through elementary perturbation methods.

Findings

Analytical solutions closely match numerical results.

Elementary perturbation methods effectively describe phase transition phenomena.

Provides a bridge between classical Landau theory and holographic approaches.

Abstract

Focusing on the connection between the Landau theory of second order phase transitions and the holographic approach to critical phenomena, we study diverse field theories in an anti-de Sitter black hole background. Through simple analytical approximations, solutions to the equations of motion can be obtained in closed form which give rather good approximations of the results obtained using more involved numerical methods. The agreement we find stems from rather elementary considerations on perturbation of Schr\"odinger equations.