Ising Model with External Magnetic Field

Hysteresis Loop and Magnetic Properties

Magnetic Hysteresis

When an external magnetic field is applied to a ferromagnetic material, the magnetization follows different paths during field increase and decrease, creating a hysteresis loop. This demonstrates magnetic memory and energy dissipation.

H = -J Σ s_i·s_j - h Σ s_i

Key Properties: Coercivity (field to demagnetize), Remanence (residual magnetization), Saturation (maximum magnetization)

Magnetization-Field Hysteresis Loop

M-H Curve showing hysteresis behavior

Spin Lattice (100×100)

Magnetization vs Time

Temperature (T): 1.50 J/k_B

External Field (h): 0.00 J

Field Sweep Rate: 0.02 J/step

Magnetization

0.00

Energy/Spin

0.00

Hysteresis Properties

Coercivity (H_c): —

Remanence (M_r): —

Saturation (M_s): —

Loop Area: — (energy dissipation)