Spin glasses and the Nobel

The Nobel Prize in physics this year was a bit of a surprise, at least to me.  As one friend described it, it's a bit of a Frankenprize, stitched together out of rather disparate components.  (Apologies for the slow post - work was very busy today.)  As always, it's interesting to read the more in-depth scientific background of the prize.  I was unfamiliar with the climate modeling of Manabe and Hasselmann, and this was a nice intro.

The other prize recipient was Giorgio Parisi, a statistical mechanician whose key cited contribution was in the theory of spin glasses, but was generalizable to many disordered systems with slow, many-timescale dynamics including things like polymers and neural networks.  

The key actors in a spin glass are excess spins - local magnetic moments that you can picture as little magnetic dipoles. In a generic spin glass, there is both disorder (as shown in the upper panel of the cartoon, spins - in this case iron atoms doped into copper - are at random locations, and that leads to a broad distribution of spin-spin interactions in magnitude and sign) and frustration (interactions such that flipping spin A to lower its interaction energy with spin B ends up raising the interaction energy with spin C, so that there is no simple configuration of spins that gives a global minimum of the interaction energy).  One consequence of this is a very complicated energy landscape, as shown in the lower panel of the cartoon.  There can be a very large number of configurations that all have about the same total energy, and flipping between these configurations can require a lot of energy such that it is suppressed at low temperatures.  These magnetic systems then end up having slow, "glassy" dynamics with long, non-exponential relaxations, in the same way that structural glasses (e.g., SiO2 glass) can get hung up in geometric configurations that are not the global energetic minimum (crystalline quartz, in the SiO2 case).  

The standard tools of statistical physics are difficult to apply to the glassy situation.  A key assumption of equilibrium thermodynamics is that, for a given total energy, a system is equally likely to be found in any microscopic configuration that has that total energy.  Being able to cycle through all those configurations is called ergodicity.  In a spin glass at low temperatures, the potential landscape means that the system can get easily hung up in a local energy minimum, becoming non-ergodic.  

An approach that Parisi took to this problem involved "replicas", where one considers the whole system as an ensemble of replica systems, and a key measure of what's going on is the similarity of configurations between the replicas.  Parisi himself summarizes this in this pretty readable (for physicists) article.  One of Parisi's big contributions was showing that the Ising spin glass model of Sherrington and Kirkpatrick is exactly solvable.

I learned about spin glasses as a doctoral student, since the interacting two-level systems in structural glasses at milliKelvin temperatures act a lot like a spin glass (TLS coupled to each other via a dipolar elastic interaction, and sometimes an electric dipolar interaction), complete with slow relaxations, differences between field-cooled and zero-field-cooled properties, etc.  

Parisi has made contributions across many diverse areas of physics.  Connecting his work to that of the climate modelers is a bit of a stretch thematically - sure, they all worry about dynamics of complex systems, but that's a really broad umbrella.  Still, it's nice to see recognition for the incredibly challenging problem of strongly disordered systems.