This is not to say that different phases always differ by symmetries! Liquids and gases have the same symmetry. In fact, one can go continuously from a liquid to a gas, by going first to high pressures and then heating. It is safe to say, though, that if the two materials have different symmetries, they are different phases.


Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).