An Analytic Analysis of Phase Transitions in Holographic Superconductors

TL;DR

This paper provides an analytical study of second-order phase transitions in holographic superconductor models, revealing universal properties, critical exponents, and relationships between critical temperature and charge density across various dimensions.

Contribution

It introduces a simple analytic framework to identify all possible second-order phase transitions and their universal characteristics in holographic superconductor models with St"uckelberg mechanism.

Findings

Critical exponents can exceed mean field value 1/2

Universal relationships between critical temperature and charge density

Analytic identification of all second-order phase transitions

Abstract

Using a simple analytic approach, we study the universal properties of second-order phase transition in holographic superconductor models. We explore a general model in arbitrary dimensions in which the condensation occurs via the St\"uckelberg spontaneous symmetry breaking mechanism. All the possible second-order phase transitions and their universal characteristics can be identified analytically. The relationship between the critical temperature and charge density is generic, and the critical exponents can be greater than the typical mean field value 1/2. In addition, the related numerical factors can also be computed qualitatively.