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

Abstract

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 ${\theta }^{\prime }$ and $\theta$ of the order parameter and the response function respectively, are calculated to the second order in $\epsilon =2\sigma -d$.

18 pages, 4 figures, 1 table