# Competing s-wave orders from Einstein-Gauss-Bonnet gravity

## TL;DR

This paper investigates the competition between two s-wave orders in a holographic superconductor model derived from Einstein-Gauss-Bonnet gravity, revealing complex phase transition behaviors including reentrant transitions near the Chern-Simons limit.

## Contribution

It introduces a detailed analysis of two s-wave order competition in Einstein-Gauss-Bonnet gravity, highlighting phase transition phenomena and the influence of the Gauss-Bonnet coefficient.

## Key findings

- Identification of intersection points in free energy curves indicating phase coexistence.
- Observation of reentrant phase transitions near the Chern-Simons limit.
- Explanation of nontrivial $T_c-\alpha$ behavior near the Chern-Simons limit.

## Abstract

In this paper, the holographic superconductor model with two s-wave orders from 4+1 dimensional Einstein-Gauss-Bonnet gravity is explored in the probe limit. At different values of the Gauss-Bonnet coefficient $\alpha$, we study the influence of tuning the mass and charge parameters of the bulk scalar field on the free energy curve of condensed solution with signal s-wave order, and compare the difference of tuning the two different parameters while the changes of the critical temperature are the same. Based on the above results, it is indicated that the two free energy curves of different s-wave orders can have one or two intersection points, where two typical phase transition behaviors of the s+s coexistent phase, including the reentrant phase transition near the Chern-Simons limit $\alpha=0.25$, can be found. We also give an explanation to the nontrivial behavior of the $T_c-\alpha$ curves near the Chern-Simons limit, which might be heuristic to understand the origin of the reentrant behavior near the Chern-Simons limit.