http://www.lassp.cornell.edu/sethna/OrderParameters/BrokenSymmetry.html Interesting view: phase changes are about symmetry changes. One counterexample to this is glasses (amorphous solids). They can be solid or liquid but no symmetry changes that I know of. The fact glasses tend to have non-sharp melting points, as opposed to a lot of other phase changes with more sharply-defined changeovers, could be argued to support his view, though(?). Another way to look at it, which also supports his view, if the "freedom of motion" in a liquid IS a symmetry. Also, for many glasses, there is a crystalline ordered phase which can form, but takes ages to do so. If so we could argue this not really a counterexample. Must such an ordered phase exist with lower energy than the disordered phase? I claim "no" and as proof I point out that certain 2D tiling problems have min-energy state (i.e. tiling) corresponding to Turing machine valid computations... which can be arbitrarily infinitely messy.