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Abstract
We have simulated lattice models of homogenous and randomly perturbed systems exhibiting continuous symmetry breaking, concentrating on domain sizes and configuration character. The system consists of rod-like objects within a cubic lattice interacting via a Lebwohl–Lasher-type interaction at temperature T, but including impurities at concentration p imposing a random anisotropy field-type disorder, coupled with anchoring strength W to neighboring host director molecules. An example of such systems represents nematic LC or nanotubes. We study molecular domain patterns as a function of p, W, T, and sample history. Histories are defined either by a temperature-quenched history (TQH), a field-quenched history (FQH) or from an annealed history (AH). Finite size-scaling is used to determine the nature of the orientational ordering correlations. We distinguish three different kinds of phase. Short ranged order (SRO) implies exponential decay of orientational correlations. Quasi-long-range order (QLRO) sustains algebraic decay of orientational correlations. True long-range order (LRO) implies a non-zero order parameter in the thermodynamic limit in the absence of an external field. In the TQH case for particular values of p and W, we find SRO or QLRO, with possible LRO at very low W and p. For FQH, in the limit of very low W and p, we observe LRO, which gives way to an SRO regime with increasing p and W. Comparing FQH and TQH histories at particular values of T, we saw QLRO and SRO respectively. The crossover between regimes depends on history, but in general, the FQH yields a more ordered phase than the AH, which in turn yields a more ordered phase than the TQH. In phases in which SRO occurs, the orientational correlation length in the weak-disorder limit obeys universal Imry-Ma scaling ξd ∼ W− 2/(4 − d).