论文标题
流动表示中二维XY模型的渗透
Percolation of the two-dimensional XY model in the flow representation
论文作者
论文摘要
我们通过蠕虫型算法模拟流动表示中的二维XY模型，直至线性系统尺寸$ L = 4096 $，并研究流程配置的几何特性。随着耦合强度$ k $的增加，我们观察到该系统经历了一个渗透过渡$ k _ {\ rm perc} $，该阶段由小簇组成，该阶段由小簇组成，进入一个有序的阶段，其中包含一个巨大的渗透集群。也就是说，在低温阶段，与与自旋特性相关的QUSI-long-long-range顺序相比，那里表现出长期的顺序。接近$ k _ {\ rm perc} $，标准有限尺寸缩放率ANSATZ为二阶相变的标准有限尺寸缩放量表很好地描述了几何观测值的缩放行为。估计的渗透阈值$ k _ {\ rm perc} = 1.105 \，3（4）$接近，但显然比Berezinskii-kosterlitz-- thouless-thouless（bkt）过渡点$ k _ {\ rm bkt} = 1.119 \，3（3（3（10）$，该$ k _ {\ rm bkt} = 1.119 \，3（10）$，并确定了promppitituus and promption and。这些非常规的观察结果引起了各种有趣的问题，它们的解决方案将在BKT相变的各种经典和量子系统上散发出灯光。
We simulate the two-dimensional XY model in the flow representation by a worm-type algorithm, up to linear system size $L=4096$, and study the geometric properties of the flow configurations. As the coupling strength $K$ increases, we observe that the system undergoes a percolation transition $K_{\rm perc}$ from a disordered phase consisting of small clusters into an ordered phase containing a giant percolating cluster. Namely, in the low-temperature phase, there exhibits a long-ranged order regarding the flow connectivity, in contrast to the qusi-long-range order associated with spin properties. Near $K_{\rm perc}$, the scaling behavior of geometric observables is well described by the standard finite-size scaling ansatz for a second-order phase transition. The estimated percolation threshold $K_{\rm perc}=1.105 \, 3(4)$ is close to but obviously smaller than the Berezinskii-Kosterlitz-Thouless (BKT) transition point $K_{\rm BKT} = 1.119 \, 3(10)$, which is determined from the magnetic susceptibility and the superfluid density. Various interesting questions arise from these unconventional observations, and their solutions would shed lights on a variety of classical and quantum systems of BKT phase transitions.
