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Relaxational processes in the one-dimensional Ising model with long-range interactions.

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Monte Carlo simulations reveal complex droplet dynamics in one-dimensional Ising models. Varying interaction decay rates (σ) showed surface dimensions distributed around effective dimensions, enhancing dynamical crossover.

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Area of Science:

  • Statistical physics
  • Condensed matter physics
  • Computational physics

Background:

  • Ordered phases in one-dimensional systems exhibit complex relaxational dynamics.
  • Long-range interactions significantly influence the behavior of these systems.
  • Understanding these dynamics is crucial for characterizing phase transitions.

Purpose of the Study:

  • Investigate relaxational processes in one-dimensional Ising models with varying interaction strengths.
  • Examine the impact of effective dimensionality on droplet dynamics.
  • Compare simulation results with droplet theory predictions.

Main Methods:

  • Monte Carlo simulations were employed to model three types of spin systems: pure ferromagnetic, diluted ferromagnetic, and spin glass.
  • The parameter σ was systematically varied to control the effective dimension by tuning the interaction decay rate.
  • Droplet dynamics were analyzed across a range of effective dimensions, from lower to upper critical values.

Main Results:

  • The surface dimension of droplets was found to be distributed around the effective dimension of the system.
  • This distribution in surface dimension leads to complex droplet dynamics.
  • Dynamical crossover phenomena were significantly enhanced due to these complex dynamics.

Conclusions:

  • The study confirms the relevance of droplet theory in describing relaxational processes in these models.
  • The effective dimension, controlled by interaction decay, plays a critical role in shaping system dynamics.
  • Complex dynamics arising from surface dimension distribution are key to understanding enhanced dynamical crossover in one-dimensional systems.