On 12/26/2012 1:36 PM, Warren Smith wrote:
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.
I don't think they are solid, they're just liquids with very high viscosity. Brent
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.
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