Energy minima and ordering in ferromagnets with static randomness.

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Computational physics

Background:

• The Imry-Ma argument predicts that random-field (RF) and random-anisotropy (RA) systems should not exhibit long-range magnetic order at finite dimensions.
• Understanding the magnetic ordering behavior of disordered systems is crucial for materials science and condensed matter physics.

Purpose of the Study:

• To investigate the magnetic ordering of 2D and 3D random-field and random-anisotropy models.
• To challenge or confirm theoretical predictions, specifically the Imry-Ma argument, through large-scale simulations.

Main Methods:

• Energy minimization at T=0 Kelvin.
• Monte Carlo simulations at temperatures above 0 Kelvin.
• Modeling of up to 150 million classical spins in 2D and 3D lattices.

Main Results:

• 3D RA models exhibit magnetic ordering upon cooling, contradicting the Imry-Ma argument.
• In 3D RA models, if anisotropy exceeds exchange interactions, magnetization is reduced, and a spin-glass component emerges.
• 3D RF systems do not magnetically order but freeze into a correlated spin-glass state due to pinned singularities.

Conclusions:

• The Imry-Ma argument's predictions for magnetic ordering in 3D RA models are challenged by simulation results.
• Singularities play a critical role in preventing magnetic ordering in 3D RF systems.
• The behavior of magnetic systems with competing interactions (exchange, random field, anisotropy) is complex and depends on their relative strengths.