Percolation of the two-dimensional XY model in the flow representation

Bao-Zong Wang, Pengcheng Hou, Chun-Jiong Huang, and Youjin Deng
Phys. Rev. E 103, 062131 – Published 21 June 2021

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 Kperc 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 Kperc, 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 Kperc=1.1053(4) is close to but obviously smaller than the Berezinskii-Kosterlitz-Thouless (BKT) transition point KBKT=1.1193(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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  • Received 28 October 2020
  • Accepted 25 May 2021

DOI:https://doi.org/10.1103/PhysRevE.103.062131

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Bao-Zong Wang1,*, Pengcheng Hou1,*, Chun-Jiong Huang2,1,†, and Youjin Deng1,3,‡

  • 1Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Science and Technology of China, Hefei 230027, China
  • 2Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong Kong, Hong Kong, China
  • 3CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

  • *These two authors contributed equally to this paper.
  • chunjiong.huang@gmail.com
  • yjdeng@ustc.edu.cn

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Issue

Vol. 103, Iss. 6 — June 2021

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