Testing theories for disordered classical systems

Alan Middleton

Department of Physics, Syracuse University, Syracuse, USA

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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