Condensed Matter Physics
Most phases of matter can be understood through the lens of spontaneous symmetry-breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small sub-set of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking rotational symmetry. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter including nematic phases of liquid crystals, charge- and spin- density waves, superfluids and many others.
There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter like fractional quantum Hall liquids, and spin-liquids. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.
Read more about this topic: Spontaneous Symmetry Breaking, Spontaneous Symmetry Breaking in Physics
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