We distinguish between the states of matter: gas, liquid and solid. Possibly we could add the plasma state and/or the superconductive state as new states of matter. Phase transistions at certain temperature perhaps with some other conditions should have to exist. What do you think, does it make sense?
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Yes, there are other phases of matter besides solid, liquid, gas, and phase transitions between these other phases work in a similar way to transitions between the more familiar phases. As another example, helium undergoes a phase transition between a "normal" fluid and a superfluid at a temperature of about 2 K.
A phase transition is a Thermodynamic (therefore bulk matter) concept which pertains to abrupt changes in the physical properties of a system which occur on a boundary of a Phase Diagram. In the classic case this Phase Diagram has axes for Temperature and Pressure. Water has the three classic phases, plus a "supercritical" region above the critical point.
In the case of Superconductivity the physical change occurs on the temperature conductivity graph, but as remarked in another Answer this is not a phase transition universal to all matter.