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Random pinning in glassy spin models with plaquette interactions.
Robert L Jack1, Ludovic Berthier
1Department of Physics, University of Bath, Bath, BA2 7AY, United Kingdom.
Summary
We studied amorphous order in glassy spin models using random pinning. Increasing pinned spins causes a crossover from relaxation to localization, revealing growing length and time scales in these systems.
Area of Science:
- Condensed matter physics
- Statistical mechanics
- Complex systems
Background:
- Amorphous order is crucial in glassy systems, but its behavior under external perturbations like pinning is not fully understood.
- Previous theoretical treatments of random pinning in glassy models often rely on approximations like mean-field or mode-coupling theories.
Purpose of the Study:
- To investigate the impact of random pinning on amorphous order in two distinct glassy spin models.
- To identify the critical concentration of pinned spins leading to system localization.
- To characterize the scaling behavior and associated length/time scales at low temperatures.
Main Methods:
- Utilizing a random pinning procedure to introduce controlled disorder in the spin models.
- Analyzing the system's relaxation dynamics and identifying crossovers in behavior.
- Examining scaling laws at low temperatures to understand the growth of amorphous order.
Main Results:
- A sharp crossover, not a thermodynamic phase transition, was observed from bulk relaxation to single-state localization as pinned spin concentration increased.
- Scaling behavior was evident in both models at low temperatures.
- The study identified the growing length and time scales associated with amorphous order and the specific fraction of pinned spins needed for localization.
Conclusions:
- Random pinning induces a distinct localization phenomenon in finite-dimensional glassy spin models, differing from mean-field predictions.
- The findings provide a new theoretical framework for understanding the effects of disorder in complex systems.
- The identified crossover and scaling behaviors offer insights into the fundamental nature of amorphous order.
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