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Multicritical behavior in models with two competing order parameters.

Astrid Eichhorn1, David Mesterházy, Michael M Scherer

  • 1Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo, N2L 2Y5 Ontario, Canada.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 16, 2013
PubMed
Summary
This summary is machine-generated.

We used the functional renormalization group to study O(N1) ⊕ O(N2) symmetric models. Our findings reveal new critical behaviors and fixed points, with implications for high-energy physics and symmetry breaking.

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Area of Science:

  • Theoretical physics
  • Condensed matter physics
  • Quantum field theory

Background:

  • Models with O(N1) ⊕ O(N2) symmetry are crucial for understanding systems with competing order parameters.
  • The behavior of such models in three dimensions is complex, featuring various critical points.

Purpose of the Study:

  • To investigate the critical behavior and fixed points of O(N1) ⊕ O(N2) symmetric models in three dimensions.
  • To analyze the stability of these fixed points and their evolution into four dimensions.
  • To explore implications for high-energy physics and the emergence of Goldstone modes.

Main Methods:

  • Nonperturbative functional renormalization group (FRG) approach.
  • Analysis of fixed points and their stability in the N1,N2 plane.
  • Dimensional continuation from three to four dimensions.

Main Results:

  • Identified distinct fixed points, including bicritical and tetracritical behavior, arising from competing order parameters.
  • Analyzed the stability of symmetry-enhanced isotropic, decoupled, and biconical fixed points.
  • Found evidence for a triviality problem in coupled two-scalar models relevant to high-energy physics.
  • Observed noncanonical critical exponents at semi-Gaussian fixed points and the emergence of Goldstone modes.

Conclusions:

  • The functional renormalization group provides a powerful tool for studying complex critical phenomena in multi-component symmetry models.
  • The competition of order parameters leads to rich critical behavior and diverse fixed points.
  • The study offers insights into fundamental questions in high-energy physics and the nature of symmetry breaking.