## Abstract

We consider a quantum two-dimensional O (N) ⊗ O (2) / O (N - 2) ⊗ O (2)_{diag} nonlinear sigma model for frustrated spin systems and formulate its 1 / N-expansion which involves fluctuating scalar and vector fields describing kinematic and dynamic interactions, respectively. The ground state phase diagram of this model is obtained within the 1 / N-expansion and 2 + ε renormalization group approaches. The temperature dependence of correlation length in the renormalized classical and quantum critical regimes is discussed. In the region ρ_{in} < ρ_{out}, χ_{in} < χ_{out} of the symmetry broken ground state (ρ_{in, out} and χ_{in, out} are the in- and out-of-plane spin stiffnesses and susceptibilities) the mass M_{μ} of the vector field can be arbitrarily small, and physical properties at finite temperatures are universal functions of ρ_{in, out}, χ_{in, out}, and temperature T. For small enough M_{μ} these properties show a crossover from low- to high temperature regime at T ∼ M_{μ}. In the region ρ_{in} > ρ_{out} or χ_{in} > χ_{out} finite-temperature properties are universal functions only at sufficiently large M_{μ}. The high-energy behaviour in the latter region is similar to the Landau-pole dependence of the physical charge e on the momentum scale in quantum electrodynamics, with mass M_{μ} playing a role of e^{-1}. The application of the results obtained to the triangular-lattice Heisenberg antiferromagnet is considered.

Original language | English |
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Pages (from-to) | 439-460 |

Number of pages | 22 |

Journal | Nuclear Physics B |

Volume | 814 |

Issue number | 3 |

DOIs | |

Publication status | Published - 21 Jun 2009 |

Externally published | Yes |

## Keywords

- 1 / N expansion
- Frustration
- Non-collinear magnetism
- Nonlinear sigma model
- Renormalization group
- Triangular lattice