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 ${\mathrm{\chi }}_{\mathrm{\perp }}$ and spin-wave velocity c for the weakly frustrated spin-1/2 square-lattice Heisenberg antiferromagnet with exchange couplings ${\mathit{J}}_1$, ${\mathit{J}}_2$, and ${\mathit{J}}_3$ to first, second, and third neighbors. By connecting ${\mathrm{\chi }}_{\mathrm{\perp }}$ 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 Néel and magnetically disordered ground states. To one-loop level in an ε expansion we find a disordering transition across a line joining the points (${\mathit{J}}_2$,${\mathit{J}}_3$)/${\mathit{J}}_1$=(0.15,0) and (0,0.09). Thus, the classical phase boundary (${\mathit{J}}_2$+2${\mathit{J}}_3$)/${\mathit{J}}_1$=1/2 is shifted asymmetrically by quantum fluctuations, as expected when the transition is to a columnar dimerized ground state.