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 $p^σ s_{p}s_{-p}$ 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 $θ^{\prime}$ and $θ$ of the order parameter and the response function respectively, are calculated to the second order in $ε=2σ-d$.