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Amid Ranjkesh Siahkal, 2014, doktorska disertacija

Opis: Structures exhibiting continuous symmetry breaking are extremely susceptible to various perturbations. The reason behind is the existence of Goldstone modes in the gauge component of the order parameter describing broken symmetry. The so-called Larkin-Imry–Ma argument claims that even infinitesimally weak random field-type disorder destroys long range order (LRO) which would otherwise be present in the absence of random disorder. Furthermore, it claims that the system breaks into domain type configuration having short range order (SRO), where the characteristic domain size scales as ksi= W^-2/(4-d). Here W measures the strength of random field interaction and d is the dimensionality of space. However, some studies claim that structures with quasi long range order (QLRO) are established instead of SRO. The main focus of this doctor thesis is the character of nematic structures in the random field. I studied theoretically and numerically nematic structures that are obtained by continuous symmetry breaking in orientational degrees of freedom on decreasing the temperature T, starting from the ordinary liquid, the so called isotropic phase. In particular, I investigated conditions for which the Larkin-Imry-Ma theorem holds true. So far statistical interpretations of such systems have typically used two different semi- microscopic type models: i) the Random Anisotropic Nematic (RAN) and ii) the Sprinkled Silica Spin (SSS) model. The RAN model is a Lebwohl-Lasher (LL) model with nematic molecules locally coupled with uncorrelated random anisotropic field at each site, while the SSS model has a finite concentration of impurities frozen in random directions. I used a three dimensional (d = 3) model intermediate between SSS and RAN models, with finite concentration p of frozen impurities, where p < pc (pc stands for the percolation threshold). The simulations were performed at different temperatures for temperature-quenched (TQH) and field-quenched histories (FQH), as well as for temperature-annealed histories (AH). The first two of these limits represent extreme histories encountered in typical experimental studies. Numerically, I studied the impact of control parameters (T, p, W) and history of samples (TQH, FQH, AH) on structural properties of the system. Within the model I was varying p, temperature T, interaction strength W and also sample histories. From final configurations, I calculated orientational order parameters and two-point correlation functions. Next, I estimated the size of the Larkin-Imry-Ma domains d. Finite size-scaling was also used to determine the range of the orientational ordering, as a function of W, p, T and sample history. The main results of my study are the following. In general, the system exhibited strong memory effects, indicating important role of history of samples. Furthermore, obtained results were relatively robust (from macroscopic point of view), indicating substantial energy barriers among competing states. On increasing the strength W, I typically obtained the following sequence of orders: LRO, QLRO, and SRO. For some concentrations p,however, SRO was absent. The crossover anchoring strength between QLRO and SRO strongly depends on history of samples, and it has the lowest values for TQH. From my simulations it follows that for the model used the Larkin-Imry-Ma argument holds only in limited range of model parameters. In most cases I obtain QLRO instead of SRO. However, in all structures there is imprint of Larkin-Imry-Ma domains, exhibiting scaling d  1/ (W2p) in the weak anchoring regime. This suggests that we do not have a “classical ” QLRO with algebraic decay with distance. Similar results were obtained in the studies of magnetic systems.
Ključne besede: nematic liquid crystals, topological defect, order parameter, symmetry breaking, domains, Random field, larkin-Imry–Ma theorem, speroNematics
Objavljeno v DKUM: 15.07.2014; Ogledov: 1892; Prenosov: 132
.pdf Celotno besedilo (2,86 MB)

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