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We analyze the zero temperature phase diagrams of the spin S quantumantiferromagnet on square and triangular lattices with competing nearest andnext-nearest exchange interactions as well as biquadratic couplings. Weapproach the problem from the large S limit. Our primary focus is ondetermining the extent to which the existence and character of any quantumdisordered phases can be inferred from this approach.

Phases of frustrated quantum antiferromagnets on the square and triangular lattices