Landau Free Energy and Analytic Tricritical Point in Holographic Superfluid

TL;DR

This paper develops an analytical approach to study the Landau free energy and tricritical point in holographic superfluids, providing exact coefficients and critical velocities, enhancing understanding of phase transitions in these models.

Contribution

It introduces a method for obtaining exact coefficients in the Landau free energy expansion of holographic superfluids, including the critical superfluid velocity at the tricritical point.

Findings

Derived exact coefficients for Landau free energy expansion.

Determined the critical superfluid velocity at the tricritical point.

Validated analytical results with numerical data.

Abstract

We investigate the analytical method in studying the holographic superfluid model which is described by Maxwell field minimally coupling to a charged scalar field in a fixed AdS black hole background. We propose a method that enables us to find exact value of coefficient in the solution and thus obtain higher-order expansion of the associated Landau free energy of the holographic superfluid with flow. We determine the critical value of superfluid velocity at the tricritical point of holographic superfluid and compare it with the numerical value.