Susceptibility and percolation in two-dimensional random field Ising magnets

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Magnetism

Background:

• The behavior of magnetic systems in the presence of random fields is crucial for understanding complex magnetic phenomena.
• The ground-state structure of two-dimensional magnets is sensitive to disorder and external influences.

Purpose of the Study:

• To investigate the ground-state structure of the two-dimensional random field Ising magnet.
• To determine how ferromagnetism vanishes and how external fields influence domain structures and susceptibility.

Main Methods:

• Exact numerical calculations were employed to study the system's ground-state properties.
• Analysis involved defining critical length scales and external field values related to percolation transitions.

Main Results:

• Ferromagnetism disappears at a system size-dependent length scale, L(b), which scales exponentially with the random field strength.
• In the presence of an external field (H), domains melt continuously for L > L(b), leading to size-independent magnetization and L-2 susceptibility decay.
• A critical external field, H(c)(delta), defines a percolation transition for spanning clusters, belonging to the standard short-range correlated percolation universality class.

Conclusions:

• Below a critical random field strength (delta(c)), systems percolate even without an external field, indicating fractal domain structures.
• The mass of spanning clusters scales with the fractal dimension of standard percolation (D(f)=91/48) at low random fields.
• The study defines new length scales related to 'red clusters,' offering further insights into the system's complex structure.