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Ordering kinetics in the random-bond XY model.

M Kumar1, S Chatterjee2, R Paul2

  • 1School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India.

Physical Review. E
|January 20, 2018
PubMed
Summary
This summary is machine-generated.

Quenched disorder slows domain growth in the random-bond XY model. In 2D, growth follows a power law, while 3D shows logarithmic growth, indicating a breakdown of superuniversality.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • The random-bond XY model is a fundamental model in statistical mechanics.
  • Understanding domain growth dynamics is crucial for characterizing phase transitions and material properties.
  • Nonconserved kinetics introduce complex temporal evolution distinct from equilibrium systems.

Purpose of the Study:

  • To investigate the impact of quenched disorder on domain growth kinetics in the XY model.
  • To determine the dimensionality dependence of domain growth exponents.
  • To examine the universality of scaling functions under disorder.

Main Methods:

  • Comprehensive Monte Carlo simulations were employed.
  • The study focused on the random-bond XY model with nonconserved kinetics.
  • Analysis included real-space correlation functions and two-time autocorrelation functions.

Main Results:

  • Quenched disorder was found to significantly slow down domain growth in both 2D and 3D.
  • In 2D, power-law domain growth with a disorder-dependent exponent was observed.
  • In 3D, an asymptotically logarithmic growth regime was identified, deviating from simple power laws.
  • Real-space correlation functions exhibited disorder-independent scaling, but two-time autocorrelation functions showed disorder dependence.

Conclusions:

  • The presence of quenched disorder alters domain growth dynamics in the random-bond XY model.
  • The observed growth regimes (power-law in 2D, logarithmic in 3D) highlight dimensionality effects.
  • The breakdown of superuniversality, evidenced by the autocorrelation function's response to disorder, is a key finding.