Phase transitions in staggered spin ladders

We map spin ladders with n(l) legs and couplings J', across all rungs and J(1 +/- gamma) along the legs, staggered in both directions, to a sigma model. Setting its theta = (2m + 1) pi (where it is known to be gapless), we locate the critical curves in the gamma versus J'/J plane at each n(l), and spin S. The phase diagram is rich and has some surprises: When two gapped chains are suitably coupled, the combination becomes gapless. With n(l), gamma, and J'/J to control, the prospects for experimentally observing any one of these equivalent transitions are enhanced. We interpret our results in the framework of the resonating valence bond description of ladders.