  In the probe limit, we study the holographic $p$-wave phase transition in the
Gauss-Bonnet gravity via numerical and analytical methods. Concretely, we study
the influences of the external magnetic field on the Maxwell complex vector
model in the five-dimensional Gauss-Bonnet-AdS black hole and soliton
backgrounds, respectively. For the two backgrounds, the results show that the
magnetic field enhances the superconductor phase transition in the case of the
lowest Landau level, while the increasing Gauss-Bonnet parameter always hinders
the vector condensate. Moreover, the Maxwell complex vector model is a
generalization of the SU(2) Yang-Mills model all the time. In addition, the
analytical results backup the numerical results. Furthermore, this model might
provide a holographic realization for the QCD vacuum instability.
