Phases of two coupled Luttinger liquids

A model of two interacting one--dimensional fermion systems (``Luttinger liquids'') coupled by single--particle hopping is investigated. Bosonization allows a number of exact statements to be made. In particular, for forward scattering only, the model contains two massless boson sectors and an Ising type critical sector. For general interactions, there is a spin excitation gap and either s-- or d--type pairing fluctuations dominate. It is shown that the same behavior is also found for strong interactions. A possible scenario for the crossover to a Fermi liquid in a many chain system is discussed.