Scaling in a temperature quench in systems with a Lifshitz point: Nonconserved and conserved order parameters

Abstract

We study the growth of an N-component (including N=1) order parameter when a system with a Lifshitz point is quenched from the homogeneous disordered state to the ordered states. We study the scaling behaviours of the structure factors for both the non-conserved and conserved order parameters in the long time limit after a quench through the Lifshitz point by using the large-N and renormalisation group (RG) methods. We construct the analogues of Allen-Cahn and Lifshitz-Slyzov growth laws for nonconserved and conserved order parameters which agree with our RG results for N=1. By extending our large-N methods to the anisotropic Lifshitz point we show that the anisotropy is relevant for the growth of the nonconserved order parameter, but irrelevant for the conserved case in the large-N limit. We discuss the effects of mode coupling terms on scaling of the structure factor for the conserved order parameter case. We also consider the ordering dynamics after a quench through an off-Lifshitz point. In a large-N set up we calculate the form of the structure factors of a non-conserved order parameter when a system is quenched from the homogeneous paramegnetic to the modulated phase. We show that after a quench from the paramegnetic to the modulated phase the form of the structure factor violates the standard form of dynamical scaling. Our results compare favourably with the available numerical results.