Project 1: Effective Interface Models with Gradient Interactions and
the Cauchy-Born Rule at Positive Temperature
Participants
Jean-Dominique Deuschel, Stephan
Luckhaus, Stefan Müller
Summary
We wish to study scalar gradient Gibbs models and atomistic models
of nonlinear elasticity. For scalar gradient Gibbs models
at moderate $\beta$ we achieved a good understanding of the
static properties in the last funding period and we now
plan to address questions related to dynamics, in particular
hydrodynamic limits and their relation with large deviations
and fluctuations. A more ambitious goal is to understand
these also at large $\beta$, where the free energy is not
everywhere strictly convex. Regarding elasticity models
we will extend the renormalization analysis initiated in the last period
to the study of correlation functions and to address the uniqueness
of the ergodic gradient Gibbs measure. Two rather ambitious
long term goals are to explore a possible extension
of the renormalization approach beyond
perturbation around a free field and the study of more
complex structures which arise, e.g., in twinning of crystals.
Achievements of the research group (funding period 2006/08):
C. Cotar, J.-D. Deuschel and S. Müller:
Strict convexity of the free energy for non-convex gradient models at moderate $\beta$
Comm. Math. Phys., to appear
preprint
C.Cotar and J.-D. Deuschel:
Decay of covariances, uniqueness of ergodic component and scaling limit for a class of $\nabla\phi$ systems with non-convex potential
preprint
F. Caravenna and J.-D. Deuschel:
Scaling limits of (1+1)-dimensional pinning models with Laplacian interaction
preprint
F. Caravenna and J.-D. Deuschel:
Pinning and wetting transition for (1+1)-dimensional fields with Laplacian interaction
Ann. Probab., to appear.
preprint