Mueller Research Group

Vortices and Topological Defects

Order Parameters

Much of physics deals with the competition between order and disorder. Energetic typically drive matter towards an ordered state: the energy of a collection of sodium atoms is minized if it forms a crystal. On the other hand, energy is not the only concept playing a role in determining the behavior of a physical system. If you are at finite temperature, then entropy favors a disordered state. Similarly, at zero temperature "quantum fluctuations" may favor a disordered state. [For example, a classical crystal has every atom localized. A corrolory of the Heisenberg uncertainty principle is that it is hard to truly localize particles. Consequently you have materials such as Helium, which remain liquid down to arbitrarily low temperatures (at least at atmospheric pressure).]

Ordered states of matter typically have more degrees of freedom than unordered states: one would not notice if you uniformly translated all of the atoms in a liquid, but such a move would be important in a crystal. The object which encodes these degrees of freedom is the "order parameter". Order parameter textures occur when the order parameter varies slowly through space. A particularly interesting form of textures are those that are topological, meaning that they require the order parameter to be discontinuous. For example a dislocation in a crystal is topological.


We have some movies of spin-1 textures at the PRA Epaps site.


Here is a gallery of some of the order parameter textures which we have found in some of our studies:

lattpic1 latpic2 newmovie
nemtst26c copy nemtst26cgood nemtst26cfine
nemtst26cbright nemtst26cstroke nemtst26cstroke2
nemtst26cmulticolor nemtst26carrows nemtst26carrows2
nemtst26c copy 1 nemtst26c copy 2 nemtst26c.realybig
nemtst26c nemtst20.ur nemtst20.run1
cloudI002 cloudI001 tstI001
tstI040.fog1 tstI040.fog2 skyrmion
vectst61 metalicskyrmi bwskyrmion
bwdoubleskyrmi tstI025 bwdoubleskyrmi2
doubleskyrmi3 orthoskyrmi orthodouble
ferB2001 ferA2001 ferH2001
ferA2107 ferA2108 doublerot1
tstI001 orthodoublerot1 orthoH
charcoalS charcoalJ tstI121
skew rotfigc rotfigb
rotfig rad fig4b
fig4a fig2b fig2a
colorintA nemtst26crev035 nemtst26b035
nemtst26rev035 nemtst26rev001highres1 Figure_1
Figure_2 Figure_3