Magnetic Domains 2D

Model: zero-temperature random-field Ising model. Each cell flips when its local field h_i = J·(mean of 4 neighbours) + H exceeds its own random switching threshold ±H_c,i (drawn around the slider value). Flips cascade as domain-wall avalanches — the microscopic origin of Barkhausen noise in real ferromagnets.

Hysteresis loop: the right-hand plot traces magnetisation M against applied field H. Loop width along the H axis is the coercive field; the M value at H = 0 after saturation is the remanence. Raising H_c widens the loop (a "harder" magnet); raising J grows larger, fewer domains.