Ground state properties of the axially frustrated quantum Heisenberg model

Abstract We apply the method of infrared bounds to the axial next-nearest-neighbor Heisenberg model on the d-dimensional hypercubic lattice to examine the existence of d - 1 -dimensional antiferromagnetic long-range order (AFLRO) in the ground state of this model. We construct an upper bound on the Fourier transformed two point correlation function at whole momentum space (infrared bounds), and prove the existence of AFLRO under certain conditions.