A uniform approach to antiferromagnetic Heisenberg spins on low-dimensional lattices

Using group theoretical methods we show for both the triangular and square lattices that in the continuum limit the antiferromagnetic order parameter lives on SO(3) without respect of the initial lattice. For the antiferromag netic chain we recover the Haldane decomposition. This order parameter inte racts with a local gauge field rather than with a global one as implicitly suggested in the literature which in our approach appears in a rather natur al manner. In fact this merely corresponds to a novel extension of the spin group by a local gauge field. This analysis based on the real division alg ebras Phd applies to low-dimension Lattices (d = 1, 2, 3, 4). (C) 2000 Else vier Science B.V. All rights reserved.