Critical Dynamics of an Interface in1+εDimensions

A model describing the relaxation dynamics of an interface of Ising-like systems is introduced. By means of renormalized field theory in $d=1+\epsilon$ dimensions the dynamic critical exponent is found as $z=2+\epsilon -\frac{1}{2}{\epsilon }^2+O\left({\epsilon }^3\right)$. 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.