Stony Brook, October 12, 2007

Order from Disorder: Phase Transitions in Condensed Matter

László Mihály Click here for link to photos

Motto: The whole is greater than the sum of its parts.

Simple particles, simple interactions. Have a lot of them (Avogadro's number, 10²³)
Ground state is ordered
Raising temperature destroys order
Process is NOT gradual; there is a sharp phase transition at T_c
Symmetry change: low temperature state more symmetric
Order parameter: Measure of symmetry change

Similar concepts - many different materials

order LESS symmetry		no order MORE symmetry
Low temperature	T_c	High temperature

Two principal versions

Second order (continuous)	First order (jump)
ferromagnet, superconductor electron localization	freezing of water boiling liquid crystals

Liquid crystals: ordering of molecules

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 LCD³

Examples: calculator, PC monitor, projector

complex, colorful domains⁴

applied widely

Ferromagnets: ordering of electron spins

North/South pole - attraction/repulsion
Disordered magnet "paramagnet"
There are all kinds of other magnets - antiferro, 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
Magnetic domains: large or small

Nobel Price in Physics, 2007

d-electron metals (transition metals): two types of electrons
Localized electrons: subject to strong ferromagnetic ordering
Free electrons: conduct electricity
Interaction causes conduction to be sensitive to the magnetization
Spin valve concept - basic science in 1988 leads to better iPOD in 2007⁵
How does it work in practice: http://www.research.ibm.com/research/demos/gmr/index.html

Thanks to:
Professor Erlend Graf, for the rotating pendulum design,
Joe Feliciano and Frank Chin, Instructional Laboratories, for all experiments.

References and list of demonstration experiments

1. Figures from the CWRU Liquid Crystal Physics and Complex Fluids Group
2. Martin Bates, University of Southampton, downloaded from here
3. From Dragon Display Technology
4. From Vance Williams, Simon Fraser University
5. From the Wikimedia Commons and Wikipedia

Experiments

Cooking a liquid crystal display
Liquid crystal thermometer sheet
Look at projector screen through polarizer filter
Ferromagnetic order and domains : compass array
Ferromagnet: dropped to copper plate
Ferromagnet: magnetic liquid
Paramagnet: oxygen is magnetic
Ginzburg-Landau theory: rotating pendulum
Look at the guts of a hard disk drive