Order parameter

An order parameter vanishes in a symmetric phase and becomes nonzero when that symmetry is spontaneously broken.

Nonconserved relaxational order-parameter dynamics has ${\partial }_t\psi =-\Gamma \delta F/\delta \psi$ plus thermal noise. Its zero-wavenumber mode may decay.

Conserved relaxational order-parameter dynamics has ${\partial }_t\varphi =M{\nabla }^2(\delta F/\delta \varphi )$ plus conserved thermal noise. Its relaxation rate vanishes as $q^2$ at small wavenumber.

A hydrodynamic mode is a long-wavelength collective mode whose decay rate tends to zero because of a conservation law. Coupling to fast nonconserved variables renormalizes its diffusivity and eigenvector.