Finite-size scaling of quasi-stationary-state temperature

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• The behavior of magnetic systems, particularly their long-lived initial states, is crucial for understanding phase transitions and critical phenomena.
• Classical inertial XY ferromagnets with long-range interactions exhibit complex dynamics influenced by dimensionality and interaction strength.

Purpose of the Study:

• To numerically investigate the temperature and duration of the quasi-stationary state in d-dimensional classical inertial alpha-XY ferromagnets.
• To analyze the dependence of these properties on interaction parameters (alpha), dimensionality (d), energy per particle (U), and system size (N).
• To verify finite-size scaling laws and their dependency on system characteristics.

Main Methods:

• First-principles numerical simulations were employed to study the alpha-XY ferromagnet model.
• Analysis focused on the temperature (T_QSS) and duration (t_QSS) of the initial quasi-stationary state.
• Finite-size scaling analysis was performed to understand system size effects.

Main Results:

• The temperature of the quasi-stationary state (T_QSS) depends on alpha, d, U, and N in the long-range regime (0 ≤ alpha/d ≤ 1).
• T_QSS shows negligible changes for dimensions d=1, 2, 3.
• Finite-size scaling T_QSS - T_infinity is proportional to 1/N^beta, where beta depends primarily on alpha/d.
• Neither T_QSS nor t_QSS scaling with N depends on U.

Conclusions:

• The study elucidates the key parameters governing the quasi-stationary state in long-range interacting magnetic systems.
• Finite-size scaling provides a robust framework for understanding system size effects, with the scaling exponent dependent on interaction range.
• The independence of scaling from U suggests universality in the finite-size behavior of these systems.