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Percolation in a three-dimensional nonsymmetric multicolor loop model.

Soumya Kanti Ganguly1,2, Sumanta Mukherjee3,4,5, Chandan Dasgupta1,6

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Monte Carlo simulations reveal critical exponents for a nonsymmetric loop model

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Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Percolation transitions are critical phenomena studied in various physical systems.
  • Nonsymmetric models present unique challenges in understanding phase transitions.
  • Regular three-dimensional lattices provide a framework for lattice-based simulations.

Purpose of the Study:

  • To analyze the percolation transition of a nonsymmetric loop model.
  • To calculate critical exponents associated with this transition.
  • To compare the findings with established models like the three-dimensional XY model.

Main Methods:

  • Monte Carlo simulations were employed for numerical analysis.
  • Finite-size scaling techniques were utilized to study the critical behavior.
  • The percolation transition temperature was investigated in relation to the thermal critical temperature.

Main Results:

  • The percolation transition temperature was found to be close to, but distinct from, the thermal critical temperature.
  • A correlation length exponent was calculated using finite-size studies.
  • The obtained correlation length exponent showed a 6% agreement with that of the three-dimensional XY model.

Conclusions:

  • The nonsymmetric loop model exhibits a distinct percolation transition.
  • The critical exponents calculated provide insights into the model's behavior.
  • The agreement with the three-dimensional XY model suggests universality or shared characteristics.