Semiclassical description of the frustrated antiferromagnetic chain.

The antiferromagnetic Heisenberg model on a chain with nearest and next nearest neighbor couplings is mapped onto the SO(3) nonlinear sigma model in the continuum limit. In one spatial dimension this model is always in its disordered phase and a gap opens to excited states. The latter form a doubly degenerate spin-1 branch at all orders in 1/N. We argue that this feature should be present in the spin-1 Heisenberg model itself. Exact diagonaliza-tions are used to support this claim. The inapplicability of this model to half-integer spin chains is discussed.