Classical infinite-range-interaction Heisenberg ferromagnetic model: metastability and sensitivity to initial...

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• The classical Heisenberg ferromagnet is a model system for studying magnetic phenomena.
• Mean-field theory predicts a second-order phase transition in this model.
• Previous studies on similar models, like the XY version, showed metastable states only near criticality.

Purpose of the Study:

• To numerically investigate the inertial classical Heisenberg ferromagnet using molecular dynamics.
• To analyze the system's behavior in the microcanonical ensemble, particularly concerning metastable states.
• To compare microcanonical simulation results with canonical ensemble predictions.

Main Methods:

• Molecular dynamics simulations were employed within the microcanonical ensemble.
• The system studied is an N-sized inertial classical Heisenberg ferromagnet with infinite-range interactions.
• Kinetic temperature and maximum Lyapunov exponent were analyzed over time and system size.

Main Results:

• Microcanonical simulations recover canonical estimates for kinetic temperature far from criticality, but show discrepancies near criticality.
• A metastable state with a duration diverging with system size (N) was observed over a broad energy range, extending to high energies.
• The maximum Lyapunov exponent in the metastable state scales with system size as N^(-kappa), with kappa ≈ 0.225.

Conclusions:

• The observed long-lived metastable state in the Heisenberg ferromagnet is a significant finding, distinct from behavior in similar models like the XY version.
• Finite-size effects appear to play a role in the discrepancies observed near the critical point.
• The study highlights the complex dynamics and emergent phenomena in classical spin models beyond equilibrium predictions.