Statics and Dynamics of Disordered Elastic Systems

Abstract

We examine here various aspects of the statics and dynamics of disordered elastic systems such as manifolds and periodic systems. Although these objects look very similar and indeed share some underlying physics, periodic systems constitute a class of their own with markedly different properties. We focus on such systems, review the methods allowing to treat them, emphasize the shift of viewpoint compared to the physics of manifolds and discuss their physics in detail. As for the statics, periodicity helps the system to retain a quasi-translational order and to be stable with respect to the proliferation of free topological defects such as dislocations. A disordered periodic system thus leads to a glass phase with Bragg peaks: the Bragg glass. On the other hand, for driven lattices, transverse periodicity allows the system to retain its glassy nature, leading to a moving glass phase. The existence of these two phases has important theoretical and experimental consequences, in particular for vortex physics in superconductors, the physical system which is mainly focused here.

36 pages; 4 figures (5 .eps files); uses lprocl.sty (included) and epsfig; To be published in ``Spin glasses and random fields'' ed. A.P. Young (World Scientific)

Cited by in corpus (10)

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• Depinning of domain walls with an internal degree of freedom
• Zero field Wigner crystal
• Temperature-induced crossovers in the static roughness of a one-dimensional interface
• Out of equilibrium dynamics of classical and quantum complex systems
• Effective temperatures out of equilibrium
• Manifolds in high dimensional random landscape: complexity of stationary points and depinning
• Field Theory of Disordered Elastic Interfaces at 3-Loop Order: Critical Exponents and Scaling Functions
• Universal correlations between shocks in the ground state of elastic interfaces in disordered media
• Specific heat of the quantum Bragg Glass