IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 25 (2013) 404201 (10pp) doi:10.1088/0953-8984/25/40/404201 Symmetry breaking in nematic liquid crystals: analogy with cosmology and magnetism R Repnik 1 , A Ranjkesh 1 , V Simonka 1 , M Ambrozic 1 , Z Bradac 1 and S Kralj 1 ,2 1 Faculty of Natural Sciences and Mathematics, University of Maribor, Koroska 160, 2000 Maribor, Slovenia 2 Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia E-mail: samo.kralj@ijs.si Received 3 January 2013, in final form 21 March 2013 Published 11 September 2013 Online at stacks.iop.org/JPhysCM/25/404201 Abstract Universal behavior related to continuous symmetry breaking in nematic liquid crystals is studied using Brownian molecular dynamics. A three-dimensional lattice system of rod-like objects interacting via the Lebwohl–Lasher interaction is considered. We test the applicability of predictions originally derived in cosmology and magnetism. In the first part we focus on coarsening dynamics following the temperature driven isotropic–nematic phase transition for different quench rates. The behavior in the early coarsening regime supports predictions made originally by Kibble in cosmology. For fast enough quenches, symmetry breaking and causality give rise to a dense tangle of defects. When the degree of orientational ordering is large enough, well defined protodomains characterized by a single average domain length are formed. With time subcritical domains gradually vanish and supercritical domains grow with time, exhibiting a universal scaling law. In the second part of the paper we study the impact of random-field-type disorder on a range of ordering in the (symmetry broken) nematic phase. We demonstrate that short-range order is observed even for a minute concentration of impurities, giving rise to disorder in line with the Imry–Ma theorem prediction only for the appropriate history of systems. 1. Introduction Static and dynamics of domains in symmetry broken phases are of interest for different branches of physics [1–4]. Understanding of and the ability to control the domain structure are important for various applications in condensed matter systems [3]. Furthermore, related physics exhibits many universalities the study of which broadens under- standing at the fundamental level [1, 2]. Namely, domain formation depends on a few basic properties of systems, independent of microscopic details [2]. Despite the underlying simplicity, some important features of domain formation remain unresolved. It is of interest to find relatively simple and experimentally accessible systems to study such open problems [1]. A phase reached via continuous symmetry breaking phase transition is at the continuum level determined by two qualitatively different fields. The degree of ordering is determined by an order-parameter field (OPF). On the other hand, the symmetry breaking ‘direction’ is described by a symmetry breaking field (SBF), also referred to as a gauge field. These fields can respond to various perturbations and/or conflicting boundary conditions on vastly different length scales. Locally perturbed OPF relaxes towards a bulk-equilibrium value on distances comparable to the order parameter correlation length ξ . In most cases ξ reflects the intrinsic ‘material’ properties of a system. In confined systems, for example, ξ might depend on the characteristic linear confinement length R if these lengths are of the same order of magnitude. On the other hand, if conflicting boundary 1 0953-8984/13/404201+10$33.00 c  2013 IOP Publishing Ltd Printed in the UK & the USA