Long-wave fluctuations of the two-dimensional Heisenberg antiferromagnet

Abstract

We have reduced the Heisenberg model for the quantum antiferromagnet in the leading approximation over 1/s to the spin-rotator model which represents some sort of quantum lattice rotator model. We perform the long-wavelength reduction of this spin-rotator model. An intermediate scale [Lambda] was introduced and the short-wavelength antiferromagnetic spin fluctuations were integrated out. As a result, we obtained the continuum nonlinear sigma model with some additional contributions. We presented arguments showing that this model is renormalizable in the framework of 1/N perturbation theory. We separated out all ultraviolet divergencies and expressed all parameters of the theory in terms of the parameters of the primary Heisenberg model, in the one-loop approximation.