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Glassy systems with frozen-in disorder present severe
challenges both for analysis and computational work.
Standard perturbation methods fail to describe these systems
and computational equilibration times are quite long.
I will start by describing general approaches which extend the
phase space of the systems, thereby avoiding metastable traps
in the free energy landscape. Field theories for pinned
manifolds, which must take into account metastability and spatial fluctuations, have been challenging to develop. One
candidate is the functional renormalization group, which keeps
an infinite number of parameters. I will describe numerical
work that directly tests the functional renormalization group
approach for scalar fields affected by random bond, random
field, and periodic disorders in a variety of dimensions. We
have computed the fixed point functions and derivatives. Our results include the predicted linear cusp, close quantitative
agreement with one-loop analysis and trends suggested by
higher-order calculations, and general physical features,
such as recent predictions for sensitivity to disorder and
correspondences with shocks in decaying Burger turbulence.
Collaborators: Pierre Le Doussal and Kay Wiese. |
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