Yes, its possible to grow most of them - but they will require certain things. Lots of water for one thing, they must not be allowed to dry out, a spot that is in shade between 11-3 pm during the day, or somewhere that only ever receives dappled sunlight, and that the roots are in a cool spot - placing thick mulch or rocks over the roots helps to achieve this. Availability of clematis where you are is another issue... and you haven't said where you are in Arizona either. There's something called the 'Sunset Western Garden Book' which will give advice on the best varieties, and if you have Baker or Whitfill nurseries, they do supply clematis (apparently...)