  We consider a two dimensional model of non-interacting chains of spinless
fermions weakly coupled via a small inter-chain hopping and a repulsive
inter-chain interaction. The phase diagram of this model has a surprising
feature: an abrupt change in the Fermi surface as the interaction is increased.
We study in detail this so called meta-nematic transition, and show that the
well-known $2 1/2-$order Lifshitz transition is the criticalndpoint of this
first order quantum phase transition. Furthermore, in the vicinity of the
endpoint, the order parameter has a non-perturbative BCS form. We also study a
competing crystallization transition in this model, and derive the full phase
diagram. This physics can be demonstrated experimentally in dipolar ultra-cold
atomic or molecular gases. In the presence of a harmonic trap, it manifests
itself as a sharp jump in the density profile.
