PHASE-DIAGRAM OF THE S=1 2 FRUSTRATED COUPLED LADDER SYSTEM/

We present a theoretical study of the magnetic phase diagram of the fr ustrated coupled ladder structure realized recently in several materia ls. This system displays a nondegenerate spin-gap state in the dimer l imit and an infinitely degenerate spin-gap state in the regime of weak ly coupled zigzag chains. Between these we demonstrate the existence o f gapless, magnetically ordered regions whose order is antiferromagnet ic close to the honeycomb lattice limit, and incommensurate along the chains when all three magnetic interactions compete.