  Using spin-wave theory, we show that geometric frustration fails to preserve
a two-dimensional spin fluid. Even though frustration can remove the interlayer
coupling in the ground-state of a classical anti-ferromagnet, spin layers
innevitably develop a quantum-mechanical coupling via the mechanism of ``order
from disorder''. We show how the order from disorder coupling mechanism can be
viewed as a result of magnon pair tunneling, a process closely analogous to
pair tunneling in the Josephson effect. In the spin system, the Josephson
coupling manifests itself as a a biquadratic spin coupling between layers, and
for quantum spins, these coupling terms are as large as the inplane coupling.
An alternative mechanism for decoupling spin layers occurs in classical XY
models in which decoupled "sliding phases" of spin fluid can form in certain
finely tuned conditions. Unfortunately, these finely tuned situations appear
equally susceptible to the strong-coupling effects of quantum tunneling,
forcing us to conclude that in general, geometric frustration cannot preserve a
two-dimensional spin fluid.

Strongly Correlated Electrons