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

TL;DR

This paper investigates the scaling behavior of order parameters after a quench through a Lifshitz point, using large-N and RG methods, revealing new growth laws and the relevance of anisotropy.

Contribution

It introduces analogues of growth laws for Lifshitz points and extends large-N analysis to anisotropic cases, highlighting the relevance of anisotropy and mode coupling effects.

Findings

Derived growth laws for nonconserved and conserved order parameters.

Showed anisotropy is relevant for nonconserved but irrelevant for conserved cases.

Identified violation of standard dynamical scaling after quenching to the modulated phase.

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.