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• W3096323404 abstract "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." @default.
• W3096323404 created "2020-11-09" @default.
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• W3096323404 date "2020-10-27" @default.
• W3096323404 modified "2023-09-27" @default.
• W3096323404 title "Percolation of the two-dimensional XY model in the flow representation" @default.
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