We study the characteristics of nematic structures in a randomly perturbed nematic liquid crystal (LC) phase. We focus on the impact of the samples history on the universal behavior. The obtained results are of interest for every randomly perturbed system exhibiting a continuous symmetry-breaking phase transition. A semimicroscopic lattice simulation is used where the LC molecules are treated as cylindrically symmetric, rod-like objects interacting via a Lebwohl-Lasher (LL) interaction. Pure LC systems exhibit a first order phase transition into the orientationally ordered nematic phase at on lowering the temperature . The orientational ordering of LC molecules is perturbed by the quenched, randomly distributed rod-like impurities of concentration . Their orientation is randomly distributed, and they are coupled with the LC molecules via an LL-type interaction. Only concentrations below the percolation threshold are considered. The key macroscopic characteristics of perturbed LC structures in the symmetry-broken nematic phase are analyzed for two qualitatively different histories at . We demonstrate that, for a weak enough interaction among the LC molecules and impurities, qualitatively different history-dependent states could be obtained. These states could exhibit either short-range, quasi-long-range, or even long-range order. 1. Introduction Domains often appear in phases of broken continuous symmetry [1, 2]. The reason behind this is causality that is a finite speed of the information propagation [3]. Consequently, in a fast enough phase transition in a different part of systems a different gauge component of the order parameter field is selected. This results in the appearance of regions in which the gauge field is essentially spatially homogeneous. These regions are referred to as domains and the mechanism of their formation as the Kibble-Zurek mechanism [4]. At boundaries between domains topological defects (TDs) [5] reside carrying a topological charge . The total topological charge of the system is conserved. At a given time, a domain pattern is well determined by a single characteristic size . The initial size of visible domains (the so-called protodomains) is dictated by the phase transition quench rate [4, 6, 7]. The domain walls are energetically costly, and, consequently, the average domain size grows with time following the scaling law , where is a universal scaling coefficient [1]. This growth is enabled by the annihilation of defects and antidefects. In ideal pure systems, a single domain would be gradually formed as a function of time.
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