Long-range order by crucial non-linear effects in Heisenberg models

Abstract

Linear spin wave theory usually provides reliable indications about the absence of long-range order (LRO) in Heisenberg models. Here the authors study the equilibrium configuration of the three-dimensional Heisenberg model with competitive interactions in the neighbourhood of the phase boundary between the ferromagnetic and helical phases where linear spin wave theory suggests the absence of LRO caused by a soft k_{perpendicular to} ⁴ behaviour of the spin wave energy in the long wavelength limit. To assess the reliability of this indication they have studied the two-magnon bound states which exist below the two-magnon band over the whole Brillouin zone in all cases where exact results assure the absence of LRO. They did not find any bound states for sufficiently small wavevectors on the ferro-helix transition line. So the authors have performed a controlled low-temperature calculation beyond the linear approximation for the spin wave spectrum and the order parameter. They have proved that non-linear contributions restore LRO in contrast with previous speculations.