Universal properties of frustrated spin systems: 1/N-expansion and renormalization group approaches

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 ρin<ρout, χin<χout of the symmetry broken ground state (ρin,out and χin,out are the in- and out-of-plane spin stiffnesses and susceptibilities) the mass Mμ of the vector field can be arbitrarily small, and physical properties at finite temperatures are universal functions of ρin,out, χin,out, and temperature T. For small enough Mμ these properties show a crossover from low- to high temperature regime at T∼Mμ. In the region ρin>ρout or χin>χout finite-temperature properties are universal functions only at sufficiently large Mμ. 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 Mμ playing a role of e−1. The application of the results obtained to the triangular-lattice Heisenberg antiferromagnet is considered.