Broken Symmetry in the world of solid

So fascinating the conception of broken symmetry!! Before this term I had thought that the broken symmetry only exist in the most elementary and theoretical physics such as the cosmology and the elementary particles which I thought interesting but not within my ability...(Maybe under the influence of A.Zee's Fearful Symmetry, illustrating the fascinating world of broken symmetry in the world of elementary particles..)

And so glad to find that in the world of condensed matter physics, the conception of broken symmetry also exist!! Not only exist, but even prevailing!!! Confirm me that I can also do some work concerning the broken symmetry someday!XDDD

Here are some notes from books concerning the broken symmetry in the world of condensed matter physics~

From P.W.Anderson's BASIC NOTIONS ON CONDENSED MATTER PHYSICS

Ch2.Broken Symmetry

• The laws that govern the particles with which we usually deal have a very high degree of symmetry: transitional, rotational, space-inversion and time-reversal. In the elementary fireball, it is supposed that the vacuum and all the particles with with their puzzling approximate symmetry of SU3, isospin, parity, etc, are the result of some cosmological phase transiton which originated from a state with some very high overall symmetry which is not manifest to us.
• In solid, the transitional symmetry is broken everywhere.

• The overwhelming majority of real physical systems with interactions between the particles tend to exhibit the phenomenon of a lowest-energy state's not having the full symmetry of space or of the Hamiltonian's describing their interactions.

• The Bose liquid break symmetry in a totally different way-for it could not be divided into independent parts, but rather have a position-dependent phase. Here the Gauge symmetry is broken.
• Broken time-reversal invariance,(ferromagnetic); Broken inversion symmetry(ferroelectric); superconductivity is also broken gauge symmetry.
• "Why"of the broken symmetry: under surprisingly general circumstances the lowest energy state of a system does not have the total symmetry group of its Hamiltonian, and so in the absence of thermal fluctuations th system assumes an unsymmetrical state.
• Remaining question for "what are the consequences": (i)discreteness of phase transitions and the resulting failure of continuation, disjointness of physical phases; (ii)development of collective excitations/fluctuations; (iii)generalized rigidity; (iv) defect structures: dissipation and topological considerations.
• The first theorem of solid-state, it is impossible to change symmetry gradually.Second order phase transition could only occur between phases of different symmetry.
• Mott transition in V2O3, which can be seen as a free-electron liquid-to-gas transition.
• Order parameter: an additional variable necessary to specify the microscopic state in the lower symmetry state.