Anisotropic honeycomb domain wall networks in uniaxial systems

Abstract A systematic study of the possibility of weakly incommensurate phases with a honeycomb domain wall network structure in uniaxial systems is presented. Competition between breathing entropy, the energy needed to tilt a domain wall, and the core energy of intersections can stabilize honeycomb phases in uniaxial systems. Two types of honeycomb networks are introduced, O -shaped and X -shaped. Breathing entropy turns out to be much weaker, compared to meander entropy, in uniaxial systems than in isotropic ones. Still, our study suggests that at the chiral melting transition the commensurate solid melts into an incommensurate fluid with a local short ranged O -shaped network order. Moreover, breathing entropy of X -shaped honeycomb networks might change the Pokrovsky-Talapov nature of the commensurate to striped incommensurate solid transition.