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Conducting-angle-based percolation in the XY model.

Yancheng Wang1, Wenan Guo, Bernard Nienhuis

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Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary
This summary is machine-generated.

This study introduces a percolation problem based on the 2D XY model, finding critical transitions and exponents that align with standard percolation theory, even at low temperatures.

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Area of Science:

  • Statistical Physics
  • Condensed Matter Physics

Background:

  • The two-dimensional XY model is a fundamental model in statistical mechanics, exhibiting rich critical phenomena.
  • Percolation theory describes the formation of clusters in random systems, with applications across various scientific fields.

Purpose of the Study:

  • To define and investigate a novel percolation problem derived from the spin configurations of the 2D XY model.
  • To determine the percolation transition points and analyze the critical behavior as a function of the conducting angle and XY coupling.

Main Methods:

  • Monte Carlo simulations were employed to study the percolation properties.
  • Finite-size scaling analysis was used to determine critical exponents and universality classes.

Main Results:

  • Percolation transitions were observed by varying the conducting angle, with transition points identified for different XY couplings.
  • The critical behavior of this XY model-based percolation aligns with standard percolation theory.
  • Critical exponents obtained through finite-size scaling match those of the 2D percolation model on a uniform substrate.

Conclusions:

  • The defined percolation problem exhibits critical behavior consistent with established percolation universality classes.
  • This framework provides insights into the interplay between spin correlations in the XY model and emergent percolation phenomena.
  • The findings hold across the temperature range, including the low-temperature phase with algebraic decay of correlations.