Spin Glass Prince Rupert's Drop

Question

Spin Glass is known to converge to its ground state under Simulated Annealing.

The word choice is especially interesting since annealing is also the name of a process performed on actual glass. However, in both cases the basic principle is the same: by gradually cooling the system, we can get it to relax into a stable, low-energy configuration.

Borrowing another concept from glass working, is there a spin glass version of a Prince Rupert's Drop? (Here's a video, too.) In other words, does rapidly cooling spin glass cause it to "freeze into" a higher energy state? If so, would this metastable state suddenly transition to a much lower energy state if a small perturbation (like a tiny $\vec H$-field) were applied?

Do non-frustrated spin systems like the square-lattice Ising model demonstrate similar properties?

This post imported from StackExchange Physics at 2015-10-19 17:08 (UTC), posted by SE-user Geoffrey

Answer 1

Perhaps this isn't quite the answer you're seeking, but you may be interested in the phenomena of thermoremanent and isothermal remanent magnetization.

Basically, if you perform a deep quench on a spin glass (i.e., freeze the spins) in a uniform external magnetic field and then, after some time, switch off the magnetic field, (or alternatively, quench first and temporarily add a field later) it turns out that the spin glass retains some internal magnetization that slowly decays with time, roughly like some power law $\exp{(-t^\alpha)}$ where $0< \alpha <1$ (as noted in on p.818 of Binder & Young's 1986 paper).

In fact, if you adopt the first procedure and keep track of how long the quenched spin glass sits in the field, it turns out that after removing the field, the decay in magnetization actually depends on how long the field was on. This is known as aging - see this paper for a more thorough investigation.

To relate back to your question about simulated annealing, the spin glass is 'mostly stuck' near whatever configuration it happened to be in just before the deep quench (presumably a configuration with lots of spins attempting to align with the field present). After removing the field, the system does undergo relaxation like in classic annealing, but perhaps on timescales of much greater lengths (hence the slow power law decay).

This post imported from StackExchange Physics at 2015-10-19 17:08 (UTC), posted by SE-user sourisse