Emergence and lifting of frustration for dipolar molecules

Ising spins on a triangular lattice are like a ``harmonic oscillator'' of geometric frustration. We address the general question of how this frustration is lifted in a system of dipolar molecules confined to 2+epsilon dimensions. When the confinement to two dimensions is strong, the dipoles arrange in a triangular lattice. Upon reduction of the confinement, the dipoles undergo a transition out of the two dimensional plane, leading to an Ising degree of freedom. Spin--lattice coupling gives rise to an effective model in terms of quantum dimers. We discuss the resulting phases and the implications to current experiments with hetero-nuclear molecules.