Generalized nonlinear sigma model approach to alternating spin chains and ladders

We generalize the nonlinear sigma model treatment of quantum spin chains to cases including ferromagnetic bonds. When these bonds are strong enough, t he classical ground state is no longer the standard Neel order and we prese nt an extension of the known formalism to deal with this situation. We stud y the alternating ferromagnetic-antiferromagnetic spin chain introduced by Hida. The smooth crossover between decoupled dimers and the Haldane phase i s semi-quantitatively reproduced. We study also a spin ladder with diagonal exchange couplings that interpolates between the gapped phase of the two-l eg spin ladder and the Haldane phase. Here again we show that there is a go od agreement between DMRG data and our analytical results.