  We predict the existence of a totally new class of phases in weakly coupled,
three-dimensional stacks of two-dimensional (2D) XY-models. These ``sliding
phases'' behave essentially like decoupled, independent 2D XY-models with
precisely zero free energy cost associated with rotating spins in one layer
relative to those in neighboring layers. As a result, the two-point spin
correlation function decays algebraically with in-plane separation. Our
results, which contradict past studies because we include higher-gradient
couplings between layers, also apply to crystals and may explain recently
observed behavior in cationic lipid-DNA complexes.
