论文标题
识别三州手性Potts模型的Huse-Fisher通用类
Identifying the Huse-Fisher universality class of the three-state chiral Potts model
论文作者
论文摘要
使用角转移矩阵重新归一化组方法，我们在方格上重新访问了三态手性Potts模型，该模型是八十年代提出的，以描述表面上的相应量过敏的过渡，并与Rydberg Atoms链上的最新实验直接相关。 Huse和Fisher建议在Potts Point附近进行手性转变，这一可能性很难绝对建立或进行数字反驳。我们的结果证实，过渡在Lifshitz点上变化了字符，该角色将Pokrosky-Talapov的线路与Potts点相距远与直接连续订购端端过渡线接近的直线。由于数值结果的准确性，我们能够将分析完全基于有效的指数，以应对已经阻碍了先前数值研究的交叉。 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 are consistent with those of a self-dual version of the model, namely correlation lengths exponents $ν_x=2/3$ in the direction of the asymmetry and $ν_y=1$ perpendicular to it, an incommensurability exponent $\bar β= 2/3 $，一种特定的热指数，可保持三态POTTS模型的值$α= 1/3 $，而动态指数$ z = 3/2 $。这些结果与在90年代重建的表面上获得的实验结果非常吻合，并阐明了Rydberg Atoms链的周期-3阶段最近的Kibble-Zurek实验。
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 transition 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 are consistent with those of a self-dual version of the model, namely correlation lengths exponents $ν_x=2/3$ in the direction of the asymmetry and $ν_y=1$ perpendicular to it, an incommensurability exponent $\bar β=2/3$, a specific heat exponent that keeps the value $α=1/3$ 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.
