|A ferromagnetic system, such as iron,
is paramagnetic at high temperatures, that is, the magnetic moments of
the molecules are oriented randomly at high temperatures. However, if we
decrease the temperature by rapidly quenching the system, the magnetic
moments becomes ordered into large domains if we wait long enough. That
is the magnetic moments are all oriented the same way leaving us with a
One of my interests is to understand
how the system gets from its high temperature randomly oriented state to
its final ordered state. This process is inherently dynamic and involves
the creation of small domains in which all the spins are oriented the same
way. These domains then grow becoming larger and larger with time until
they reach macroscopic scales. This process is called domain growth or
phase ordering dynamics. I study this process both via computer simulations
(the figures below show a simulation of the domain growth process -- time
increases from left to right) as well as using analytic methods.
Although this process is relatively
simple to describe, it leads to many surprising results. For example, the
domain growth process exhibit dynamical scaling. That is, if I take one
of the figures below and shrink it by an appropriate factor, it would look
statistically the same as the domain structure at earlier times. Another
consequence of the dynamical scaling is that the characteristic domain
size grows as a power law in time.
I am now working on more realistic
models of the domain growth process. For example, domain growth is extremely
important in the crystallization process. In this case the quench is from
a high temperature liquid state to a low temperature ordered crystalline
state. Technologically it is often important to make the crystalline domains
as large as possible or grow them as quickly as possible. This domain growth
process is also important in the unmixing of insoluble liquids as well
as the spots seen on leopards.
A computer simulation of the domain coarsening of a magnetic system
after the quench. The first figure shows the small domains formed immediately
after. These domains grow until finally the system is all of one phase.
The times are (from first to last) t=1000, t=4000, t=16000 and
t=65000 iterations after the quench.
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