Effective-action approach to the frustrated Heisenberg antiferromagnet in two dimensions.

Abstract

We study the weakly frustrated two-dimensional antiferromagnetic Heisenberg model with first- (${\mathit{J}}_{1}$), second- (${\mathit{J}}_{2}$), and third-neighbor (${\mathit{J}}_{3}$) exchanges. In the limit of low frequencies and long wavelengths the effective action is identified as the O(3) nonlinear \ensuremath{\sigma} model with an additional Berry phase. Use of renormalization-group methods allows us to estimate the stability of the N\'eel phase for the square and honeycomb lattices. For the spin-1/2 square lattice an analysis at the one-loop level suggests an upper bound for the disordering transition at (${\mathit{J}}_{2}$+2${\mathit{J}}_{3}$)/${\mathit{J}}_{1}$=0.22\ifmmode\pm\else\textpm\fi{}0.04, substantially below the estimate from O(1/S) spin-wave theory. Our analysis further indicates that the spin-1/2 disordered ground state is degenerate at weak frustration, with a fourfold degeneracy for the square lattice and a threefold degeneracy for the honeycomb lattice.