Phase transitions in a holographic superfluid model with non-linear terms beyond the probe limit

TL;DR

This paper investigates how non-linear self-interaction terms and back-reaction effects influence phase transitions in a holographic superfluid model, revealing universality and the critical role of back-reaction strength in determining transition order.

Contribution

It extends holographic superfluid models by including full back-reaction and higher-order non-linear terms, analyzing their combined effects on phase transition types and universality.

Findings

Back-reaction influences phase transition order similarly to non-linear terms.

Universal behavior of phase transitions with 4th and 6th power terms in finite back-reaction.

Identification of a critical parameter $ ext{\lambda}_s$ controlling transition order.

Abstract

We study the holographic s-wave superfluid model with 4th and 6th power self-interaction terms $\lambda |\psi|^4$ and $\tau |\psi|^6$ with considering the full back-reaction of the matter fields on the metric in the 3+1 dimensional bulk. The self-interaction terms are good at controlling the condensate to realize various phase transitions, such as the zeroth-order, first-order, and second-order phase transitions within the single condensate s-wave superfluid model. Therefore, in this work, we are able to investigate the influence of the back-reaction strength on the various phase transitions, including the zeroth and first order phase transitions. In addition, we confirm that the influence of the 4th and 6th power terms on the superfluid phase transition in the case of finite back-reaction are qualitative the same as in the probe limit, thus present universality. We also plot the special value $\lambda_s$ of the parameter $\lambda$ at different back-reaction strength, below which the condensate grows to an opposite direction and is important in controlling the order of the superfluid phase transitions. Comparing the influence of the back-reaction parameter and that of the higher-order nonlinear coefficients, we see that the back-reaction strength brings in both the effective couplings similar to the 4th power and 6th power terms.