Fate of zero-temperature Ising ferromagnets

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Computational physics

Background:

• Ising ferromagnets are fundamental models in statistical mechanics.
• Understanding relaxation dynamics is crucial for phase transitions and material properties.
• Zero-temperature dynamics simplifies analysis but presents unique challenges.

Purpose of the Study:

• To investigate the relaxation dynamics of homogeneous Ising ferromagnets on finite lattices.
• To analyze the influence of lattice dimensionality on reaching the ground state.
• To characterize the long-term behavior and emergent states in these systems.

Main Methods:

• Simulations of zero-temperature spin-flip dynamics on finite lattices.
• Analysis of relaxation pathways and time scales.
• Examination of system behavior across different dimensions (2D and >2D).

Main Results:

• On square lattices, the ground state is reached most of the time, with a notable frozen two-stripe state occurring ~30% of the time.
• Asymptotic relaxation in 2D is governed by two distinct time scales, influenced by a long-lived diagonal stripe defect.
• In dimensions greater than two, the probability of reaching the ground state diminishes rapidly with increasing system size.
• Systems in higher dimensions typically become trapped in sets of metastable states, exhibiting stochastic 'blinking' behavior.

Conclusions:

• Lattice dimensionality significantly impacts the relaxation dynamics and ultimate state of Ising ferromagnets.
• The presence of defects and metastable states plays a critical role in long-time behavior, especially in higher dimensions.
• Finite-size effects and topological defects can lead to deviations from ideal ground state attainment.