Yes, definitely. In physics, we speak of many different phases of matter. Any different states which have some qualitatively different feature are different phases. An example of a qualitative difference would be the presence or absence of large-scale magnetism, or of the less familiar type of electronic order found in a superconductor. The conversion between different phases occurs under well-defined conditions of temperature, pressure, magnetic field, etc., and is called a phase transition.
The familiar phase transitions discussed in high school (among gas, liquid, and solid) are a small subset of the many transitions possible. For example, solids can exist in may different crystal structures, with phase transitions between them. So really there isn't a single solid phase, but a large family of solid phases.
There are in fact several distinct types of superconducting order, constituting different phases. Likewise there are phase transitions in and out of various magnetic phases, etc.
(published on 09/04/2010)