non-equilibrium dynamical properties of Spin glasses.

"Remanence" behaviour

As we’ve already seen (and discuss more fully in section 4.8), a spin glass in the absence of a magnetic field has zero magnetization. But it shouldn’t be surprising that when placed inside a uniform magnetic field, the atomic magnetic moments will try to orient themselves along the field—as occurs in any magnetic system—resulting in a net magnetization. So far not very exciting; but what then happens after the field is removed or altered?

There are any number of ways in which this can be done, and in the spin glass they all lead to somewhat different outcomes.

One approach is to cool the spin glass in a uniform magnetic field H from a temperature above T f to one well below, and then remove the field. On doing so, the spin glass at first retains a residual internal magnetization, called the thermoremanent magnetization. The thermoremanent magnetization decays with time, but so slowly that it remains substantial on experimental timescales.

Another procedure is to cool the spin glass below T f in zero field, turn on a field after the cooling stops, and after some time remove the field. This gives rise to the isothermal remanent magnetization.

Memory effects

In the simplest of these, a spin glass is cooled to a temperature below T f in an external magnetic field, often through a deep thermal quench. The spin glass then sits at that fixed field and temperature for a certain “waiting time” $t_w$ . After the waiting time has elapsed, the field is switched off and the decay of the thermoremanent magnetization is measured at constant temperature. Interestingly, the spin glass “remembers” the waiting time: a change in the rate of decay occurs at a time roughly $t_w$ after the field is removed. Aging is not confined to spin glasses, but their unusual behaviors make them somewhat special.

Theory of non-equilibrium behaviour of spin glasses

all share the features of a wide range of relaxational processes, leading to a broad distribution of intrinsic relaxation times; a significant amount of metastability, meaning that most relaxations, whether involving a small or large number of spins, can only occur after the system surmounts some energy or free energy barrier; and a consequently compli- cated “energy landscape,” the meaning of which is discussed in section 4.9.

Spin-Flip Dynamics of the Curie-Weiss Model: Loss of Gibbsianness with Possibly Broken Symmetry