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Size-stretched exponential relaxation in a model with arrested states.

Vaibhav Gupta1,2, Saroj Kumar Nandi1, Mustansir Barma1

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Summary

We investigated a model with competing interactions quenched to zero temperature. The system exhibits stretched exponential relaxation, with relaxation times diverging with system size, differing from typical glassy dynamics.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Kinetically constrained models (KCMs) are crucial for understanding slow dynamics in disordered systems.
  • Glassy dynamics often exhibit stretched exponential relaxation, but the underlying mechanisms can vary.
  • Competing interactions in physical models can lead to complex emergent behaviors.

Purpose of the Study:

  • To investigate the effects of a rapid quench to zero temperature on a model with competing interactions.
  • To characterize the relaxation dynamics and identify the universality class of the model.
  • To compare the observed dynamics with those of known kinetically constrained models and glassy systems.

Main Methods:

  • Simulating a model with competing interactions undergoing conserved spin dynamics.
  • Analyzing the spatial and temporal correlation functions.
  • Investigating the system's behavior in both steady state and coarsening regimes.
  • Comparing dynamics across different system sizes (L) and time scales (t).

Main Results:

  • The model exhibits stretched exponential relaxation, characterized by exp[-(t/τ_{L})^{1/2}].
  • Relaxation time (τ_{L}) scales linearly with system size (L), and τ_{L} diverges as a power of L.
  • Spatial correlation function decays as exp(-2r/sqrt[L]) in the steady state.
  • Two growing length scales, L(t_{w})∼t_{w}^{1/2} and R(t_{w})∼t_{w}^{1/4}, are observed in the coarsening regime.
  • A significant difference exists between the autocorrelation function of a single sample and the ensemble-averaged one, with the latter showing power-law decay.

Conclusions:

  • The model, while belonging to the KCM class, displays unique dynamics distinct from typical glasses.
  • The system-size-dependent relaxation time and specific correlation function forms provide a detailed characterization.
  • The observed differences in autocorrelation functions highlight the importance of sample-specific histories in such systems.