Chaos and residual correlations in pinned disordered systems

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Disordered Systems

Background:

• Elastic systems in random potentials exhibit complex behavior, including phenomena like depinning and chaos.
• Understanding the interplay between disorder correlations and system properties is crucial for predicting material behavior.

Purpose of the Study:

• To investigate the impact of mutually correlated random potentials on two copies of an elastic system.
• To analyze the short- and large-scale displacement correlations and their dependence on disorder characteristics.
• To explore the role of functional renormalization in characterizing chaos exponents and phase transitions.

Main Methods:

• Functional renormalization group (FRG) techniques were employed to study the elastic system.
• The analysis focused on decorrelation at short scales and mutual displacement correlations at large scales.
• Specific models, including random bond interfaces and the Bragg glass model, were examined.

Main Results:

• Short-scale decorrelation is governed by a boundary layer regime with chaos exponents.
• Large-scale correlations scale as [x - x']^(2zeta-mu), where mu relates to roughness exponents.
• Short-range disorder leads to positive mu, while long-range (random field) disorder exhibits no chaos (mu=0) and new fixed points.

Conclusions:

• The type of disorder significantly influences the correlation functions and the presence of chaos in elastic systems.
• Functional renormalization reveals distinct behaviors for short-range and long-range disorder, with implications for phase transitions.
• The study introduces new functional renormalization fixed points for random field disorder, offering deeper insights into depinning phenomena.