  We study in detail the phase structure of a holographic p-wave superconductor
model in a five dimensional Einstein-Maxwell-complex vector field theory with a
negative cosmological constant. To construct complete phase diagrams of the
model, we consider both the soliton and black hole backgrounds. In both two
cases, there exist second order, first order and zeroth order phase
transitions, and the so-called "retrograde condensation" also happens. In
particular, in the soliton case with the mass of the vector field being beyond
a certain critical value, we find a series of phase transitions happen such as
"insulator/superconductor/insulator/superconductor", as the chemical potential
continuously increases. We construct complete phase diagrams in terms of
temperature and chemical potential and find some new phase boundaries.
