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

TL;DR

This paper uses the renormalisation group to analyze the short-time critical dynamics of a long-range interacting Ginzburg-Landau model, deriving scaling laws and exponents after a temperature quench.

Contribution

It provides a second-order calculation of initial slip exponents for the model with long-range interactions, extending understanding of critical dynamics.

Findings

Derived asymptotic scaling laws for the model

Calculated initial slip exponents to second order in epsilon

Analyzed relaxation dynamics after a temperature quench

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 $\epsilon=2\sigma-d$.