The short-time critical behaviour of the Ginzburg-Landau model with long-range interaction

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 $p^{\sigma }{s}_p{s}_{-p}$ 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 ${\theta }^{\mathrm{\prime }}$ and $\theta$ of the order parameter and the response function respectively, are calculated to the second order in $ϵ=2\sigma -d$.