  For N impenetrable particles in one dimension where only the nearest and
next-to-nearest neighbours interact, we obtain the complete spectrum both on a
line and on a circle. Further, we establish a mapping between these N-body
problems and the short-range Dyson model introduced recently to model
intermediate spectral statistics in some systems using which we compute the
two-point correlation function and prove the absence of long-range order in the
corresponding many-body theory. Further, we also show the absence of
off-diagonal long-range order in these systems.
