Phase-field simulations demonstrate that the polarization order-parameter field in the GinzburgLandau-Devonshire model of rhombohedral ferroelectric BaTiO3 allows for an interesting linear defect, stable under simple periodic boundary conditions. This linear defect, termed here as Ising line, can be described as about 2 nm thick intrinsic paraelectric nanorod acting as a highly mobile borderline between finite portions of Bloch-like domain walls of the opposite helicity. These Ising lines play the role of domain boundaries associated with the Ising-to-Bloch domain wall phase transition.PACS numbers: 77.80.Dj, Perovskite ferroelectrics are the key materials in the current ferroelectric research and a considerable effort was recently devoted to the investigations of their domain structure and their domain wall properties. Much less is known about ferroelectric line defects, although this topic is also gaining attention [1-5, 7-11, 33], for example, in relation to magnetic vortices and skyrmions [1,2]. Ferroelecric domains and line defects may be inspiring in other research areas, too, for example in the particle physics [12].One of the most intriguing recent result in this field is the prediction of so-called Bloch-like domain walls in BaTiO 3 and PbTiO 3 , based on Ginzburg-LandauDevonshire model [13][14][15][16] and first-principles calculations [17,18]. Previously, we and others studied [211]-oriented 180-degree domain walls in the rhombohedral BaTiO 3 , separating domains with spontaneous polarization parallel and antiparallel to [111] (as usual we refer to the cubic axes of the parent paraelectric phase of BaTiO 3 , see Fig. 1 a). Calculations carried out within the Ginzburg-Landau-Devonshire model of Refs. 19,20 suggest that this domain wall has a Bloch-like (bistable and chiral) structure [13,16]. At the same time, it has been shown that this ([211]-oriented) Bloch-like wall can be transformed to an achiral, Ising-like domain wall by a moderate uniaxial stress [15]. The transformation proceeds as a continuous, symmetry-breaking phase transition associated with the divergence of dielectric permittivity [21] and with disappearance of the polarization P DW within the domain wall interior [15]. The internal domain wall polarization P DW , existing only up to the Bloch-to-Ising transition point, is parallel or antiparallel to [011] direction. It is natural to ask whether the antiparallel P DW states could coexist within the same domain wall plane, similarly as the ferroelectric domains may coexist in the bulk of ferroelectric crystal [16,[22][23][24].In our previous work [15] we have studied the case when the P DW vector has an opposite orientation within neighboring domain walls, as indicated in Fig. 1 b. Such domain structure contains only the domain walls of the same helicity and it is thus a chiral structure as a whole. In contrast, in the present work we have explored a racemic domain structure, which contains an equal amount of left-handed and right-handed areas on average as well as within each domain wa...