2D Ferroelectric Domain Avalanches (Random-Field Ising Model)

Piezoelectric ceramics like PZT are ferroelectric: every unit cell in the perovskite lattice carries a built-in electric dipole, and neighboring cells lock together into domains that flip under an applied field. This 2D simulator models that switching with a random-field Ising model — a grid of domains where each cell has its own disorder-broadened coercive threshold and is coupled to its immediate neighbors, so flipping one domain can tip its neighbors past their own threshold and trigger a cascading "avalanche" of flips, the same mechanism behind Barkhausen noise in magnetic and ferroelectric materials. Sweep the applied field by hand or automatically to trace the resulting polarization-field (P–E) hysteresis loop, and use the coupling slider to go from independent, uncorrelated domain flips (J=0) to strongly cooperative switching with large avalanches and a squarer loop.