The renormalisation group approach is applied to the study of the short-time critical behaviour of the d-dimensional Ginzburg-Landau model with long-range interaction of the form p σ s p s −p in momentum space. Firstly the system is quenched from a high temperature to the critical temperature and then relaxes to equilibrium within the model A dynamics. The asymptotic scaling laws and the initial slip exponents θ ′ and θ of the order parameter and the response function respectively, are calculated to the second order in ǫ = 2σ − d.

The theoretical renormalization-group approach is applied to the study of the short-time critical behavior of the Ginzburg-Landau model with long-range random impurities which have a power-like correlation r ÀðdÀqÞ . The system initially at a high temperature is firstly quenched to the critical temperature T c and then released to an evolution with a model A dynamics. The asymptotic scaling laws are studied in the frame of a double expansion in E ¼ 4 À d and d ¼ E þ q with d of the order of E. The initial slip exponent q 0 for the order parameter is calculated up to the first order in E ¼ 4 À d or in E 1=2 corresponding to different fixed points, respectively. For d < 4, the short-time behavior of the order parameter is investigated in one loop. Two different logarithmic and exponential-logarithmic corrections to short-time behaviors of both the autocorrelation and the order parameter are also solved in d ¼ 4 dimension. Crossover between the nonrandom behavior and quenched behavior is found for n ¼ 4 (where n is the spin dimensionality) in d ¼ 4 dimension.