RFIM, Barkhausen noise, disorder-driven phase transition, Sethna-Dahmen avalanche statistics
H_RFIM = −J Σ⟨ij⟩ sᵢsⱼ − Σᵢ (H + hᵢ)sᵢ; hᵢ ~ N(0,R²)
Critical disorder Rc≈2.16J (3D): below Rc — macroscopic jump; above Rc — smooth hysteresis
The RFIM models magnetic systems with quenched disorder (hᵢ = random local field). At T=0, avalanches occur when spins flip due to external field H sweeping. Critical disorder Rc separates macroscopic (first-order-like) from continuous (critical) behavior. At Rc: power-law avalanche size distribution P(s)~s^(-τ) with τ≈1.6 (Sethna et al 1993). Barkhausen noise in magnets is the experimental realization. Connected to depinning, crackling noise, and SOC.