Short-time critical behavior affected by weakly long-range interactions

The theoretic renormalization group approach is applied to the study of sho rt-time critical behavior of the Ginzburg-Landau model with weakly long-ran ge interactions p(sigma)s(p)s-(p). The system initially at a high temperatu re is firstly quenched to the critical temperature T-c and then released to an evolution with a model A dynamics. A double expansion in epsilon = 2 si gma - d and alpha = 1 - sigma /2 with alpha of order epsilon is employed, w here d is the spatial dimension. The asymptotic scaling laws and the initia l slip exponents theta' and theta for the order parameter and the response function respectively are calculated to the second order in epsilon for sig ma close to 2.