Curie Transition in a Ferroelectric — Landau Free-Energy Landscape

This simulator renders the Landau–Devonshire free-energy landscape F(P) = a(T−T_c)P² + bP⁴ − EP that governs a ferroelectric crystal's polarization, and lets you drive it with an oscillating field while sweeping temperature through the Curie point. A ball representing the instantaneous polarization rolls and switches wells under damped Landau–Khalatnikov dynamics, an instanced grid of dipole arrows shows the same polarization at the unit-cell level, and a live P–E plot traces the resulting hysteresis loop — which opens into a full loop below T_c and collapses to a straight line above it, exactly as a real PZT or BaTiO₃ sample does when heated through its transition.