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The ground state properties of spin-1/2 ladders are studied, emphasizing therole of frustration and ring exchange coupling. We present a unified fieldtheory for ladders with general coupling constants and geometry. Rich phasediagrams can be deduced by using a renormalization group calculation forladders with in--chain next nearest neighbor interactions and plaquette ringexchange coupling. In addition to established phases such as Haldane, rungsinglet, and dimerized phases, we also observe a surprising instability towardsan incommensurate phase for weak interchain couplings, which is characterizedby an exotic coexistence of self-consistent ferromagnetic andanti-ferromagnetic order parameters.

Competing phases in spin ladders with ring exchange and frustration