Memory effects in randomly perturbed systems exhibiting continuous symmetry breaking

Abstract

We studied pattern characteristics in randomly perturbed structures exhibiting continuous symmetry breaking. A Lebwohl–Lasher‐type lattice model was used which described well the onset of orientational ordering of a system of rod‐like objects. For example, such systems mimic the orientational ordering tendency in liquid crystals or in an ensemble of nanotubes. We set impurities to impose a random anisotropy type of disorder on the objects. Structural characteristics were studied as a function of concentration of impurities, interaction strength w between impurities and rod‐like objects, external ordering strength and history of samples. We showed that the characteristic linear size of patterns and range of ordering strongly depend on the history of samples for weak enough strength w. The two‐dimensional and three‐dimensional simulations yielded qualitatively similar results.