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Zero-temperature coarsening in the two-dimensional long-range Ising model.

Henrik Christiansen1, Suman Majumder1, Wolfhard Janke1

  • 1Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.

Physical Review. E
|June 17, 2021
PubMed
Summary
This summary is machine-generated.

We studied how the Ising model behaves after a sudden temperature change. The growth exponent remains around 3/4, differing from nearest-neighbor models, and a key relation between exponents holds true.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • Investigating nonequilibrium dynamics is crucial for understanding systems far from equilibrium.
  • Zero-temperature coarsening in models with long-range interactions exhibits unique behaviors.
  • The Ising model is a fundamental model for studying magnetism and phase transitions.

Purpose of the Study:

  • To analyze the nonequilibrium dynamics of the 2D nonconserved Ising model with power-law decaying long-range interactions after a quench to zero temperature.
  • To estimate key nonequilibrium exponents: growth exponent (α), persistence exponent (θ), and fractal dimension (df).
  • To explore the dependence of these exponents on the interaction decay parameter (σ).

Main Methods:

  • Numerical simulations of the 2D nonconserved Ising model with tunable long-range interactions (∝1/rd+σ).
  • Analysis of coarsening dynamics and calculation of nonequilibrium exponents.
  • Comparison of results across different values of σ.

Main Results:

  • The growth exponent (α) is found to be approximately 3/4, independent of σ, and distinct from the nearest-neighbor value of 1/2.
  • In the large σ regime, only the fractal dimension (df) matches the nearest-neighbor Ising model results.
  • The relation d-df=θ/α is confirmed for all studied σ, indicating its general validity.

Conclusions:

  • The growth dynamics of the long-range Ising model differ significantly from short-range models, especially for smaller σ.
  • The persistence exponent is directly linked to the growth exponent through a universal scaling relation.
  • This study validates a proposed scaling relation for persistence exponents in nonequilibrium systems with tunable interactions.