Description of magnetic short-range order in the 2D Heisenberg model:: Auxiliary fermions with reduced self-consistency

Critical magnetic fluctuations in the two-dimensional spin 1/2 quantum Heisenberg antiferromagnet (QHAF) are studied at low temperature. Spin operators are represented by fermions, and the local constraint onto the physical subspace is treated approximately as a global one. The 2D fluctuations have to be treated self-consistently beyond mean field. We propose and compare two appropriate schemes: the first one is analogous to the well-known FLEX, based on self-consistent fermion propagators, the other avoids renormalising the (unphysical) fermion, while retaining the magnetic susceptibility a self-consistent quantity. Both reproduce the correlation length xi(T) similar to exp(aJ/T) and the critical slowing down, but only the latter, 'minimal' self-consistent approximation (MSCA) yields propagating spinwave like modes, characteristic of short-range order at length scales