Weakly frustrated spin-1/2 Heisenberg antiferromagnet in two dimensions: Thermodynamic parameters and the stability of the Néel state

Using a Schwinger-boson mean-field theory, we calculate the low-temperature uniform transverse susceptibility χ_⊥ and spin-wave velocity c for the weakly frustrated spin-1/2 square-lattice Heisenberg antiferromagnet with exchange couplings J₁, J₂, and J₃ to first, second, and third neighbors. By connecting χ_⊥ and c to the bare coupling of the nonlinear {σ} model that describes the long-wavelength limit of the antiferromagnet, we are able to improve upon earlier renormalization-group estimates of the zero-temperature phase boundary separating N\'eel and magnetically disordered ground states. To one-loop level in an {ε} expansion we find a disordering transition across a line joining the points (J₂,J₃)/J₁=(0.15,0) and (0,0.09). Thus, the classical phase boundary (J₂+2J₃)/J₁=1/2 is shifted asymmetrically by quantum fluctuations, as expected when the transition is to a columnar dimerized ground state.