  We investigate a many-body wave function for particles on a cylinder known as
Laughlin's function. It is the power of a Vandermonde determinant times a
Gaussian. Our main result is: in a many-particle limit, at fixed radius, all
correlation functions have a unique limit, and the limit state has a
non-trivial period in the axial direction. The result holds regardless how
large the radius is, for fermions as well as bosons. In addition, we explain
how the algebraic structure used in proofs relates to a ground state
perturbation series and to quasi-state decompositions, and we show that the
monomer-dimer function introduced in an earlier work is an exact, zero energy,
ground state of a suitable finite range Hamiltonian; this is interesting
because of formal analogies with some quantum spin chains.
