Phase transitions in a holographic <i>s</i>+<i>d</i> model from 4D Einstein–Gauss–Bonnet gravity

Abstract In this work, the phase structure of a holographic s + d model with quartic potential terms from 4D Einstein–Gauss–Bonnet gravity is studied in the probe limit. We first show the q d − μ phase diagram with a very small value of the Gauss–Bonnet coefficient α = 1 × 10 −7 and in the absence of the quartic terms to locate the suitable choice of the value of q d , where the system admits coexistent s + d solutions. Then we consider the various values of the Gauss–Bonnet coefficient α and present the α − μ phase diagram to show the influence of the Gauss–Bonnet term on the phase structure. We also give an example of the re-entrant phase transition which is also realized in the holographic s + s and s + p models. After that we confirm the universality of the influence of the quartic term with coefficient λ d on the d -wave solutions, which is similar to the case of s -wave and p -wave solutions previously studied in the s + p model. Finally we give the dependence of the special values of the quartic term coefficient λ d on the Gauss–Bonnet coefficient α , below which the d -wave condensate grows to an opposite direction at the (quasi-)critical point, which is useful in realizing first order phase transitions in further studies of the holographic d -wave superfluids.