The 1/N Expansion and Long Range Antiferromagnetic Order

Abstract

The staggered magnetization of the Heisenberg antiferromagnet in two dimensions can be systematically approximated by a 1/N expansion. Cancellation between self energy diagrams leads to a Luttinger-like theorem for the ground state. We prove (for a smooth enough self energy) that the long range order of mean field theory ($N$=$\infty$) survives corrections to all orders of 1/N. Divergences of this series provides a new route to the disordered phases of quantum antiferromagnets.