Percolation of the two-dimensionalXYmodel in the flow representation,Physical Review E

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Percolation of the two-dimensionalXYmodel in the flow representation
Physical Review E ( IF 2.2 ) Pub Date : 2021-06-21 , DOI: 10.1103/physreve.103.062131
Bao-Zong Wang ₁ , Pengcheng Hou ₁ , Chun-Jiong Huang _{1,

2} , Youjin Deng _{1,

3}

Affiliation

We simulate the two-dimensional

X Y

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_{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 quasi-long-range order associated with spin properties. Near

K_{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_{perc} = 1.105 3 (4)

is close to but obviously smaller than the Berezinskii-Kosterlitz-Thouless (BKT) transition point

K_{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 light on a variety of classical and quantum systems of BKT phase transitions.

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