Using the corner-transfer matrix renormalization group approach, we revisit the three-state chiral Potts model on the square lattice, a model proposed in the eighties to describe commensurate-incommensurate transitions at surfaces, and with direct relevance to recent experiments on chains of Rydberg atoms. This model was suggested by Huse and Fisher to have a chiral transition in the vicinity of the Potts point, a possibility that turned out to be very difficult to definitely establish or refute numerically. Our results confirm that the transition changes character at a Lifshitz point that separates a line of Pokrosky-Talapov transitions far enough from the Potts point from a line of direct continuous order-disorder transition close to it. Thanks to the accuracy of the numerical results, we have been able to base the analysis entirely on effective exponents to deal with the crossovers that have hampered previous numerical investigations. The emerging picture is that of a new universality class with exponents that do not change between the Potts point and the Lifshitz point, and that appear to be consistent with those of a self-dual version of the model, namely correlation lengths exponents ${\nu }_x=2/3$ in the direction of the asymmetry and ${\nu }_y=1$ perpendicular to it, an incommensurability exponent $\overline{\beta }=2/3$, a specific heat exponent that keeps the value $\alpha =1/3$ of the three-state Potts model, and a dynamical exponent $z=3/2$. These results are in excellent agreement with experimental results obtained on reconstructed surfaces in the nineties, and shed light on recent Kibble-Zurek experiments on the period-3 phase of chains of Rydberg atoms.

使用角转移矩阵重归一化组方法，我们重新研究了方格上的三态手性Potts模型，该模型是在80年代提出的，用于描述表面上的等距过渡，并且与最近在Rydberg链上进行的实验直接相关原子。Huse和Fisher建议此模型在Potts点附近具有手性过渡，这种可能性很难用数字确定或反驳。我们的结果证实，在Lifshitz点处的过渡变化特征将距离波兰人点足够远的Pokrosky-Talapov过渡线与靠近它的直接连续有序-无序过渡线分隔开。由于数值结果的准确性，我们已经能够将分析完全基于有效指数来处理阻碍先前数值研究的交叉。新出现的情况是新的普适性类别，其指数在Potts点和Lifshitz点之间不变，并且似乎与该模型的自对偶版本的那些一致，即相关长度指数${\nu }_X=\mathrm{2个}/3$ 在不对称的方向上 ${\nu }_{ÿ}=\mathrm{1个}$ 垂直于它，不可通约指数 $\overline{\beta }=\mathrm{2个}/3$，保持该值的比热指数 $\alpha =\mathrm{1个}/3$ 状态的三态Potts模型和动力学指数 $ž=3/\mathrm{2个}$。这些结果与90年代在重建表面上获得的实验结果非常吻合，并为最近在Rydberg原子链的3期相上进行的Kibble-Zurek实验提供了启示。