4.2 Article

Commensurate-incommensurate transition in the chiral Ashkin-Teller model

Journal

PHYSICAL REVIEW RESEARCH
Volume 4, Issue 1, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevResearch.4.013093

Keywords

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Funding

  1. Swiss National Science Foundation

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In this study, we investigated the classical chiral Ashkin-Teller model on a square lattice using the corner transfer matrix renormalization group algorithm. We found that the melting of the period-4 phase depends on the coefficient of the four-spin term. The system exhibits different commensurate-incommensurate transitions and a critical floating phase depending on the model parameters.
We 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.

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