Frustrated two-dimensional quantum Heisenberg antiferromagnet at low temperatures

We analyze the low-temperature properties of the square-lattice quantum Heisenberg antiferromagnet, frustrated by nearest-neighbor diagonal couplings (${\mathit{J}}_{1\mathrm{-}}$ ${\mathit{J}}_2$ model), by use of Takahashi’s variational spin-wave approach. Explicit formulas are obtained for the energy, specific-heat coefficient, spin-stiffness constant, uniform susceptibility, and correlation length, as well as for the static spin-spin correlators for arbitrary values of the frustration parameter α=${\mathit{J}}_2$/${\mathit{J}}_1$. These results are compared with the available numerical results for 0<α<1. All quantities, mentioned above, change smoothly in the entire region 0<α<0.6. So, no special behavior is observed for 0.5<α<0.6. On the other hand, a sharp growth of the specific-heat coefficient in the region 0.6<α<0.7 is seen. In the extremely low-temperature limit, the present theory predicts a first-order phase transition from the disordered-Néel phase to the Ising-ordered phase, discussed by Chandra, Coleman, and Larkin.