Ferroelectric Domains — 2D Ginzburg–Landau Field

This simulator solves the polarization of a ferroelectric crystal as a genuine spatial field P(x,y,t) on a 2D lattice, using the time-dependent Ginzburg–Landau equation γ∂P/∂t = −(2aP+4bP³−E)+κ∇²P — the same Landau–Devonshire double well as the single-domain model, now coupled to its neighbours by a domain-wall energy term. Driven by an oscillating field while temperature sweeps through the Curie point, the lattice nucleates, grows and annihilates domains of opposite polarization exactly as a real polycrystalline ferroelectric does, and the macroscopic P–E hysteresis loop traced on the right is the lattice-averaged response of that whole domain ensemble rather than one particle's switch.