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Published on: September 29, 2011
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Nonuniversality of Aging during Phase Separation of the Two-Dimensional Long-Range Ising Model
Fabio Müller1, Henrik Christiansen1,2, Wolfhard Janke1
1Institut für Theoretische Physik, <a href="https://ror.org/03s7gtk40">Universität Leipzig</a>, IPF 231101, 04081 Leipzig, Germany.
Physical Review Letters
|December 23, 2024
Summary
Physical aging in a 2D Ising model with long-range interactions shows complex behavior. The autocorrelation exponent (λ) depends on interaction range (σ), with distinct values for nearest-neighbor, long-range, and intermediate regimes.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Phase Transitions
Background:
- Investigating phase-separation kinetics is crucial for understanding material properties.
- The two-dimensional conserved Ising model provides a fundamental framework for studying critical phenomena.
- Long-range interactions significantly alter system dynamics compared to short-range models.
Purpose of the Study:
- To analyze the aging properties of phase-separation kinetics in a 2D Ising model with power-law decaying long-range interactions.
- To determine the dependence of the autocorrelation exponent (λ) on the interaction decay exponent (σ).
- To explore the crossover behavior in the intermediate interaction range.
Main Methods:
- Utilizing Metropolis Monte Carlo simulations.
- Developing and employing a novel algorithm optimized for long-range interacting systems.
- Analyzing the two-time autocorrelation function C(t, t_w) to quantify aging dynamics.
Main Results:
- Observed physical aging characterized by a power-law decay of the autocorrelation function.
- Determined a specific value of λ=3.500(26) for the nearest-neighbor limit (σ→∞).
- Found λ values compatible with ≈4 in the long-range regime (σ<1) and a continuous, nonuniversal crossover for 1≲σ≲2.
Conclusions:
- The aging exponent (λ) exhibits a complex, continuous dependence on the interaction range (σ).
- The study highlights the significant impact of long-range interactions on phase-separation kinetics.
- The developed simulation algorithm enables efficient study of such complex systems.
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