Abstract: We study the typical domain size and configuration
character of a randomly perturbed system exhibiting continuous
symmetry breaking. As a model system we use rod-like objects
within a cubic lattice interacting via a Lebwohl–Lasher-type
interaction. We describe their local direction with a headless unit
director field. An example of such systems represents nematic LC or
nanotubes. We further introduce impurities of concentration p, which
impose the random anisotropy field-type disorder to directors. We
study the domain-type pattern of molecules as a function of p,
anchoring strength w between a neighboring director and impurity,
temperature, history of samples. In simulations we quenched the
directors either from the random or homogeneous initial
configuration. Our results show that a history of system strongly
influences: i) the average domain coherence length; and ii) the range
of ordering in the system. In the random case the obtained order is
always short ranged (SR). On the contrary, in the homogeneous case,
SR is obtained only for strong enough anchoring and large enough
concentration p. In other cases, the ordering is either of quasi long
range (QLR) or of long range (LR). We further studied memory
effects for the random initial configuration. With increasing external
ordering field B either QLR or LR is realized.