• North/South pole - attraction/repulsion
• There are all kinds of other magnets - amtiferro, ferri, etc.
• Electrons:
• charge (in metals electrons can move)
• spin, or magnetic moment, or "microscopic magnet" (in magnets spins are ordered)
• Ferromagnetic interaction: spins want to point in the same direction
• Order parameter: average of spin directions (magnetization)
• T_c: Curie temperature (varies, 60F for gadolinium)
• Fluctuations in space and time: illustrated by Ising model
• Magnetic domains: large or small

Liquid crystals

• Long organic molecules in solvent¹
• Various degrees of ordering: disordered, nematic, smectic and more
• Interaction: molecules need space
• Order parameter²: average direction (NO difference between N/S!)
• Changes polarized light, responds to electric field
• "twisted nematic" is used in LCD
• Examples: calculator, PC monitor, projector
• complex, colorful domains
• applied widely

• Electrons in metals interacting in another way.
• Two properties
  • Zero resistance
  • Meissner effect
• Needs really low temperatures (77K ~ -321F)
• Magnetic field kills superconductivity
• Interaction: attraction between electrons Order parameter: density of superconducting electrons
• Symmetry breaking: happens in the wavefunction of the electrons

• Perovskite crystal lattice: SrTiO₃
• Atom in the center is positive, others are negative, perfect balance
• Center atom moves in any of the 12 directions, dipole moment is created
• May be more complex, but always similar to ferromagnet
• Interaction: attraction between atoms
• Order parameter: displacement of the center atom
• Domain walls respond to electric field, visible under microscope³