Critical dynamics near dimension two for time-dependent Ginzburg-Landau models

A dynamics is introduced, via a stochastic equation of motion for $n$-component ($n>\mathrm{}2\mathrm{}$) order-parameter systems near two dimensions. The resulting time-dependent Ginzburg-Landau model with a soft constraint is studied for its critical behavior by several methods. We obtain the dynamic exponent as $z=4-\eta$ for the case of a conserved order parameter and, to two-loop order, as $z=2+c\eta$ with $c=\epsilon [1-\ln (\frac{4}{3}\left)\right]$ for the nonconserved case.