2D Ginzburg-Landau Field: Domain Coarsening & Goldstone Spin Waves

The 0D Landau model of spontaneous symmetry breaking puts a single ball on a Mexican-hat free-energy surface; the real materials it describes — ferromagnets, superconductors, superfluids — are extended in space, and that changes the physics in ways a single particle cannot show. This simulator promotes the order parameter to a full field on a 2D lattice, each site coupled to its neighbours through a genuine Ginzburg-Landau gradient term, and integrates the resulting relaxational (Model A) dynamics with thermal noise in real time. Cool the field below T_c and watch domains of a spontaneously chosen angle nucleate and coarsen against each other; seed a vortex–antivortex pair to see the topological defects that only exist because the order parameter lives in more than zero dimensions; and use the amplitude/Goldstone kick buttons to see the two normal modes directly — one gapped, one exactly massless at long wavelength, with the Goldstone mode's real k-dependent stiffness on display via the spatial coupling slider.