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Universal critical coupling constants for the three-dimensional n-vector model from field theory.

A I Sokolov1, E V Orlov, V A Ul'kov

  • 1Department of Physical Electronics, Saint Petersburg Electrotechnical University, Professor Popov Street 5, St. Petersburg 197376, Russia.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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This study estimates critical coupling constants for the O(n) model using renormalization group (RG) methods. The RG approach achieved high accuracy for g6, but showed divergence for g8.

Area of Science:

  • Theoretical physics
  • Condensed matter physics

Background:

  • The O(n)-symmetric model is crucial for understanding critical phenomena.
  • Renormalization group (RG) methods are essential for analyzing universal properties of physical systems near critical points.

Purpose of the Study:

  • To estimate universal critical values of renormalized coupling constants (g6 and g8) for the O(n)-symmetric model in three dimensions.
  • To assess the accuracy and convergence of the RG approach for these constants.

Main Methods:

  • Utilizing the field-theoretical renormalization group (RG) approach in three dimensions.
  • Calculating RG series for g6 and g8 to four- and three-loop approximations, respectively.
  • Resumming the RG series using the Padé-Borel-Leroy technique.

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Main Results:

  • Numerical estimates for the critical coupling constant g*6 were obtained with high accuracy (≤0.3%) by optimizing the shift parameter.
  • The RG expansion for g8 exhibited stronger divergence, leading to less precise numerical estimates.

Conclusions:

  • The renormalization group approach provides accurate estimates for critical coupling constants like g6.
  • The method's effectiveness can vary depending on the specific coupling constant and its series divergence.