Anisotropic deformation of the 6-state clock model: Tricritical-point classification

The two-dimensional $q$-state clock models exhibit the Berezinskii-Kosterlitz-Thouless (BKT) transition for $q\geq5$ since they are a subset of isotropic XY model. We examine $6$-state model with an anisotropic deformation. Selecting Potts as source deformation, naturally violates discrete rotational symmetry introduce deformation parameter $\alpha$ in interpolating ($\alpha = 1$) and 0$) models. employ corner transfer matrix renormalization group method to analyze phase transitions on square lattice thermodynamic limit. Three different phases identified. diagram is constructed, we determine tricritical point at $\alpha_{\rm c} 0.21405(4)$ $T_{\rm 0.834017(5)$. Analyzing latent heat entanglement entropy vicinity c}(\alpha_{\rm c})$, observe single discontinuous two BKT meeting point. exhibits second order critical exponents $\beta \approx 1/10$ $\delta 14$. conjecture that infinitesimal surrounding consists three fundamental transitions, which first orders gradually weaken into second-order