ANTIFERROMAGNETIC SPIN LADDERS WITH ODD AND EVEN NUMBERS OF CHAINS

We construct frustrated antiferromagnetic spin ladders with m chains f or which the exact ground state can be determined in a particular para meter regime. The excitation spectrum is shown rigorously to be gaples s (with gap) for odd (even) m. In a general parameter regime, the four -chain and periodic ladders are studied using a mean-field theory base d on the bond operator formalism for spin S=1/2. The excitation spectr um and the spin gap are calculated in both the cases. The spin gap of the frustrated ladder system has a larger magnitude than in the case o f nonfrustrated ladders. For the frustrated periodic ladder, the spin gap vanishes at a critical value of the interladder coupling strength which is larger than the critical value in the case of nonfrustrated p eriodic ladders.