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

We consider a quantum two-dimensional O(N) circle times O(2)/O(N - 2) circle times 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 + epsilon renormalization group approaches. The temperature dependence of correlation length ill the renormalized classical and quantum critical regimes is discussed. In the region rho(in) < rho(out), chi(in) < chi(out) of the symmetry broken ground state (rho(in,out) and chi(in,out) are the in- and out-of-plane spin stiffnesses and susceptibilities) the mass M-mu of the vector field call be arbitrarily small, and physical properties at finite temperatures are universal functions of rho(in,out), chi(in,out), and temperature T. For small enough M-mu these properties show a crossover from low- to high temperature regime at T similar to M-mu, In the region rho(in) > rho(out) or chi(in) > chi(out) finite-temperature properties are universal functions only at sufficiently large M-mu. 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-mu playing a role of e(-1). The application of the results obtained to the triangular-lattice Heisenberg antiferromagnet is considered. (C) 2009 Elsevier B.V. All rights reserved.