Phases of frustrated quantum antiferromagnets on the square and triangular lattices

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