<Landau theory> treats the <order parameter> as spatially uniform and expands the free-energy density in powers allowed by its symmetries. The <Landau-Ginzburg theory> promotes it to a field $\phi(\mathbf x)$ and adds gradient terms such as $|\nabla\phi|^2$. It therefore describes spatial fluctuations, interfaces, defects, and <correlation length>[correlation lengths], while reducing to Landau theory for uniform fields.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 303 / 1 / a / Solution

 Solution (source code)