As a note, the in-canon explanation for why they work is that Unobtanium, (I thought it was funny. ) which composes most of the mountain, is a room-temperature (or higher) superconductor, and the Meisner effect means that it excludes Pandora's magnetic field, and so levitates.
However, each mountain is, well... mountain-sized, and easily weighs thousands of tons. They also float what is quite clearly multiple of hundreds of metres, if not multiple kilometres off the ground. My intuition says that, at some point, the Meisnerr effect must fail and leave the mountain to crash to the floor, but I can't really explain why that would happen or what the result would be, re: superconductivity. Is anyone here more knowledgeable?
As a bonus question, are there any physically conceivable properties that