| Popis: |
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 + e 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. |
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