论文标题
六状态时钟模型的各向异性变形：三位临界分类
Anisotropic deformation of the 6-state clock model: Tricritical-point classification
论文作者
论文摘要
二维$ q $ - 状态时钟模型显示了Berezinskii-Kosterlitz- thouless（BKT）的过渡，以$ Q \ geq5 $，因为它们是各向异性XY型号的子集。我们检查了具有各向异性变形的$ 6 $状态时钟模型。该模型选择$ 6 $ - 状态的Potts模型作为变形的来源，自然违反了时钟模型的离散旋转对称性。我们在时钟模型中介绍了各向异性变形参数$α$，将时钟插值（$α= 1 $）和potts（$α= 0 $）型号。我们采用角传递矩阵重新归一化组方法来分析热力学极限中平方晶格上的相变。确定了三个不同的阶段和相变。构造了相图，我们确定了一个三级临界点，在$α_ {\ rm c} = 0.21405（4）$和$ t _ {\ rm c} = 0.834017（5）$。分析$ t _ {\ rm c}附近的潜热和纠缠熵（α_ {\ rm c}）$，我们观察到一个单个不连续的相变和两个BKT相位过渡在三个智力点中的交流。三边形点显示了第二阶的相变，其临界指数$β\约1/10 $和$δ\ \ \ \ \ \ \ \约14 $。我们猜想，三边形点的无限围绕由三个基本相变组成，其中第一个和BKT订单逐渐削弱到二阶三智度点。
The two-dimensional $q$-state clock models exhibit the Berezinskii-Kosterlitz-Thouless (BKT) transition for $q\geq5$ since they are a subset of the isotropic XY model. We examine the $6$-state clock model with an anisotropic deformation. Selecting the $6$-state Potts model as a source of the deformation, the model naturally violates the discrete rotational symmetry of the clock model. We introduce the anisotropic deformation parameter $α$ in the clock model interpolating the clock ($α= 1$) and the Potts ($α= 0$) models. We employ the corner transfer matrix renormalization group method to analyze the phase transitions on the square lattice in the thermodynamic limit. Three different phases and phase transitions are identified. The phase diagram is constructed, and we determine a tricritical point at $α_{\rm c} = 0.21405(4)$ and $T_{\rm c} = 0.834017(5)$. Analyzing the latent heat and the entanglement entropy in the vicinity of the $T_{\rm c}(α_{\rm c})$, we observe a single discontinuous phase transition and two BKT phase transitions meeting in the tricritical point. The tricritical point exhibits a phase transition of the second order with the critical exponents $β\approx 1/10$ and $δ\approx 14$. We conjecture that an infinitesimal surrounding of the tricritical point consists of the three fundamental phase transitions, in which the first and the BKT orders gradually weaken into the second-order tricritical point.
