Stein: Research on Disordered and Random Materials (for Physicists)
My research (in collaboration with Charles Newman,
and sometimes others) addresses the mathematical foundations of
theory of condensed matter systems with quenched disorder; we are particularly,
but not exclusively, interested in the class of disordered magnets known
as spin glasses.
Although there exist proposed solutions of idealized (and unrealistic)
spin glass models, in particular those with infinite-ranged interactions,
our interests center on answering fundamental statistical mechanical
questions that bear on the behavior of real laboratory spin glasses.
These questions, many of which remain controversial despite two decades
of intensive study, include the nature of ordering in the equilibrium
spin glass phase (assuming one exists), understanding anomalous dynamical
behavior, such as slow relaxation and aging arising from nonequilibrium
dynamics, and proving the presence or absence of a phase transition
in finite dimensions.
The methods used and concepts introduced should be relevant not only
for spin glasses but also for other disordered systems, many of which
remain poorly understood. Moreover, the generality of our approach should