Renormalization-group relaxational dynamics of interfaces in4−εdimensions

Abstract

We present a dynamic renormalization-group calculation in $4\ensuremath{-}\ensuremath{\epsilon}$ dimensions of the capillary wave dispersion relation ${\ensuremath{\omega}}_{q}$ for the interface of an Ising-like system driven by relaxational dynamics (model A). The dispersion relation is of the form ${\ensuremath{\omega}}_{q}=\ensuremath{-}i\ensuremath{\Gamma}{q}^{z}\ensuremath{\Omega}(q\ensuremath{\xi})$, with $\ensuremath{\Omega}(x)$ universal and $z=2+O({\ensuremath{\epsilon}}^{2})$, and satisfies the Goldstone theorem for the spontaneously broken Euclidean symmetry.