Abstract
We simulate the two-dimensional model in the flow representation by a worm-type algorithm, up to linear system size , and study the geometric properties of the flow configurations. As the coupling strength increases, we observe that the system undergoes a percolation transition 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 , 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 is close to but obviously smaller than the Berezinskii-Kosterlitz-Thouless (BKT) transition point , 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.
3 More- Received 28 October 2020
- Accepted 25 May 2021
DOI:https://doi.org/10.1103/PhysRevE.103.062131
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