  We show that three dimensional "sliding" analogs of the Kosterlitz-Thouless
phase, in stacked classical two-dimensional XY models and quantum systems of
coupled Luttinger Liquids, can be enlarged by the application of a parallel
magnetic field, which has the effect of increasing the scaling dimensions of
the most relevant operators that can perturb the critical sliding phases.
Within our renormalization group analysis, we also find that for the case of
coupled Luttinger liquids, this effect is interleaved with the onset of the
integer quantum Hall effect for weak interactions and fields. We comment on
experimental implications for a conjectured smectic metal phase in the
cuprates.
