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Order-parameter scaling in fluctuation-dominated phase ordering.

Rajeev Kapri1, Malay Bandyopadhyay2, Mustansir Barma3

  • 1Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, Sector 81, Knowledge City, S. A. S. Nagar, Manauli 140306, India.

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Systems with many order parameters, like sliding particles on surfaces, require analyzing Fourier modes for phase ordering. This study reveals static and dynamic scaling laws for these modes, uncovering temporal intermittency in coarse-grained depth models.

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Area of Science:

  • Statistical physics
  • Complex systems

Background:

  • Systems with fluctuation-dominated phase ordering often need multiple order parameters to describe their state.
  • Hard-core sliding particles on fluctuating surfaces and coarse-grained depth (CD) models exemplify such systems.

Purpose of the Study:

  • To investigate the static and dynamic scaling laws of long-wavelength Fourier components of the density profile in these models.
  • To characterize the order parameter set and its behavior during phase ordering.

Main Methods:

  • Analysis of static and dynamic scaling laws for Fourier modes (Q_{mL}).
  • Studying probability distributions P(Q_{mL}) and time-dependent correlation functions.
  • Investigating dynamical structure functions and flatness for temporal intermittency.

Main Results:

  • Static scaling laws were found for mean Fourier modes with exponents ϕ≃2/3 (EW), ϕ≃3/5 (KPZ), and ϕ≃3/4 (CD model).
  • Probability distributions and correlation functions exhibit scaling behavior with dynamic exponent z=2 (EW) and z=3/2 (KPZ).
  • The CD model demonstrates temporal intermittency.

Conclusions:

  • The study successfully characterizes phase ordering in complex systems using multiple order parameters.
  • Scaling laws provide a robust framework for understanding system dynamics, including temporal intermittency in CD models.