Critical Dynamics of an Interface in1+εDimensions

Abstract

A model describing the relaxation dynamics of an interface of Ising-like systems is introduced. By means of renormalized field theory in $d=1+\ensuremath{\epsilon}$ dimensions the dynamic critical exponent is found as $z=2+\ensuremath{\epsilon}\ensuremath{-}\frac{1}{2}{\ensuremath{\epsilon}}^{2}+O({\ensuremath{\epsilon}}^{3})$. Interpolation with the known result near four dimensions yields good agreement with a high-temperature expansion and with recent real-space and Monte Carlo renormalization-group calculations in two dimensions.