Nyckees, SamuelMila, Frederic2022-02-282022-02-282022-02-282022-02-0410.1103/PhysRevResearch.4.013093https://infoscience.epfl.ch/handle/20.500.14299/185784WOS:000752828100002We investigate the classical chiral Ashkin-Teller model on a square lattice with the corner transfer matrix renormalization group algorithm. We show that the melting of the period-4 phase in the presence of a chiral perturbation takes different forms depending on the coefficient of the four-spin term in the Ashkin-Teller model. Close to the clock limit of two decoupled Ising models, the system undergoes a two-step commensurate-incommensurate transition as soon as the chirality is introduced, with an intermediate critical floating phase bounded by a Kosterlitz-Thouless transition at high temperature and a Pokrovsky-Talapov transition at low temperature. By contrast, close to the four-states Potts model, we argue for the existence of a unique commensurate-incommensurate transition that belongs to the chiral universality class, and for the presence of a Lifshitz point where the ordered, disordered, and floating phases meet. Finally, we map the whole phase diagram, which turns out to be in qualitative agreement with the 40-year-old prediction by Huse and Fisher.Physics, MultidisciplinaryPhysicsphase-diagramasymmetric clocktransfer-matrixdomain-wallspotts-modelmonte-carlorenormalizationtext::journal::journal article::research article