Kinetics of the two-dimensional long-range Ising model at low temperatures

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• The two-dimensional Ising model describes magnetic phenomena.
• Domain growth kinetics are crucial for understanding phase transitions.
• Long-range interactions introduce complex dynamics.

Purpose of the Study:

• Investigate low-temperature domain growth kinetics in the 2D Ising model with long-range coupling.
• Analyze the impact of quenching to zero temperature (T=0) versus non-zero temperatures (T>0).
• Determine the universality of the growth exponent at T=0.

Main Methods:

• Theoretical analysis of domain growth dynamics.
• Extended Monte Carlo simulations.
• Analytical arguments for single domain behavior.

Main Results:

• At T>0, growth exponent z follows Bray-Rutenberg predictions (z=1+σ for σ<1, z=2 for σ>1).
• At T=0, long-range interactions cause interface drift, leading to peculiar dynamics.
• A universal growth exponent z=4/3 is found at T=0, independent of σ.

Conclusions:

• Quenching to T=0 significantly alters domain growth kinetics compared to T>0.
• The growth exponent at T=0 is a universal quantity.
• Findings are supported by both simulation and theoretical analysis.