Freezing of dynamical exponents in low dimensional random media.

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Disordered systems

Background:

• Understanding the behavior of particles in random potentials is crucial for various fields.
• The study of dynamical transitions and glass phases is a complex area in physics.

Purpose of the Study:

• To investigate the dynamical transition of a particle in a random potential with logarithmic correlations in dimensions d=1,2.
• To analyze the relationship between static and dynamic properties in disordered systems.

Main Methods:

• Exact results in d=1 for the dynamical transition temperature and dynamical exponent.
• Analytical arguments for d=2, extending findings to related systems like the 2D random gauge XY model.
• Analysis of freezing mechanisms involving energy barriers and valleys.

Main Results:

• A dynamical transition occurs at a positive temperature T(dyn)>0.
• In d=1, T(dyn) equals the static glass transition temperature T(c).
• The dynamical exponent z(T) exhibits distinct behaviors in high-temperature and glass phases, with similar formulas proposed for d=2.

Conclusions:

• Dynamical freezing is predicted in the studied systems, including the 2D random gauge XY model.
• In d=1, a mapping between dynamics and statics reveals freezing involves both barriers and valleys.
• Anomalous scaling in creep dynamics has implications for understanding dislocation motion.