  We continue to study the holographic p-wave superconductor model in the
Einstein-Maxwell-complex vector field theory with a non-minimal coupling
between the complex vector field and the Maxwell field. In this paper we work
in the AdS soliton background which describes a conformal field theory in the
confined phase and focus on the probe approximation. We find that an applied
magnetic field can lead to the condensate of the vector field and the AdS
soliton instability. As a result, a vortex lattice structure forms in the
spatial directions perpendicular to the applied magnetic field. As a
comparison, we also discuss the vector condensate in the Einstein-SU(2)
Yang-Mills theory and find that in the setup of the present paper, the
Einstein-Maxwell-complex vector field model is a generalization of the SU(2)
model in the sense that the vector field has a general mass and gyromagnetic
ratio.
